Condensed matter physics, area laws & LQG?

[atyy]

marcus posted this intriguing paper that the boundary state in LQG is mixed! I'm not sure this is related to the concerns of this thread, but given that one way of getting a mixed state is via entanglement and a reduced density matrix, I thought I'd post it here too.

http://arxiv.org/abs/1306.5206
The boundary is mixed
Eugenio Bianchi, Hal M. Haggard, Carlo Rovelli
(Submitted on 21 Jun 2013)
We show that Oeckl's boundary formalism incorporates quantum statistical mechanics naturally, and we formulate general-covariant quantum statistical mechanics in this language. We illustrate the formalism by showing how it accounts for the Unruh effect. We observe that the distinction between pure and mixed states weakens in the general covariant context, and surmise that local gravitational processes are indivisibly statistical with no possible quantal versus probabilistic distinction.

 

[atyy]

Maldacena's talk at Strings 2013.

Entanglement and spacetime geometry
Talk: http://www.youtube.com/embed/C1NX8baM9vw
Slides: http://strings2013.sogang.ac.kr/design/default/data/juan_maldacena.pdf

On slide 25 he writes: " If one accepts very "quantum geometries" ". (Translation: if one accepts LQG;)

Let me also note the talk by Myers on RG Flows, Entanglement and Holography. It's very related to the concerns of this thread, but rather technical, so I mention it mainly because he has one LQG paper;)

 

[Haelfix]

On slide 25 he writes: " If one accepts very "quantum geometries" ". (Translation: if one accepts LQG;)

What they have is a very special state (the thermofield state) where they can make a kinda/sorta/not really analogy between ER and EPR. They also argue that this holds for small perturbations away from the thermofield state. Only here do they have anything that resembles a classical geometry.

For highly quantum states (say a spin singlet system) there is no obvious classical geometry, and so if you believe the ER=EPR story, the corresponding right hand side must be described by some sort of quantum geometry, who's precise form is unknown.

 

[atyy]

http://arxiv.org/abs/1307.1132
The holographic dual of an EPR pair has a wormhole
Kristan Jensen, Andreas Karch
(Submitted on 3 Jul 2013)
We construct the holographic dual of two colored quasiparticles in maximally supersymmetric Yang-Mills theory entangled in a color singlet EPR pair. In the holographic dual the entanglement is encoded in a geometry of a non-traversable wormhole on the worldsheet of the flux tube connecting the pair. This gives a simple example supporting the recent claim by Maldacena and Susskind that EPR pairs and non-traversable wormholes are equivalent descriptions of the same physics.

http://arxiv.org/abs/1307.1367
Spacetime emergence via holographic RG flow from incompressible Navier-Stokes at the horizon
Stanislav Kuperstein, Ayan Mukhopadhyay
(Submitted on 4 Jul 2013)
We show that holographic RG flow can be defined precisely such that it corresponds to emergence of spacetime. We consider the case of pure Einstein's gravity with a negative cosmological constant in the dual hydrodynamic regime. The holographic RG flow is a system of first order differential equations for radial evolution of the energy-momentum tensor and the variables which parametrize it's phenomenological form on hypersurfaces in a foliation. The RG flow can be constructed without explicit knowledge of the bulk metric provided the hypersurface foliation is of a special kind. The bulk metric can be reconstructed once the RG flow equations are solved. We show that the full spacetime can be determined from the RG flow by requiring that the horizon fluid is a fixed point in a certain scaling limit leading to the non-relativistic incompressible Navier-Stokes dynamics. This restricts the near-horizon forms of all transport coefficients, which are thus determined independently of their asymptotic values and the RG flow can be solved uniquely. We are therefore able to recover the known boundary values of almost all transport coefficients at the first and second orders in the derivative expansion. We conjecture that the complete characterisation of the general holographic RG flow, including the choice of counterterms, might be determined from the hydrodynamic regime.

 

[atyy]

http://arxiv.org/abs/0908.0591
A condensed matter interpretation of SM fermions and gauge fields
I. Schmelzer
(Submitted on 5 Aug 2009)
We present the bundle Aff(3) x C x /(R^3), with a geometric Dirac equation on it, as a three-dimensional geometric interpretation of the SM fermions. Each C x /(R^3) describes an electroweak doublet. The Dirac equation has a doubler-free staggered spatial discretization on the lattice space Aff(3) x C (Z^3). This space allows a simple physical interpretation as a phase space of a lattice of cells in R^3. We find the SM SU(3)_c x SU(2)_L x U(1)_Y action on Aff(3) x C x /(R^3) to be a maximal anomaly-free special gauge action preserving E(3) symmetry and symplectic structure, which can be constructed using two simple types of gauge-like lattice fields: Wilson gauge fields and correction terms for lattice deformations. The lattice fermion fields we propose to quantize as low energy states of a canonical quantum theory with Z_2-degenerated vacuum state. We construct anticommuting fermion operators for the resulting Z_2-valued (spin) field theory. A metric theory of gravity compatible with this model is presented too.

http://arxiv.org/abs/1208.0206
Tensor Network and Black Hole
Hiroaki Matsueda, Masafumi Ishihara, Yoichiro Hashizume
(Submitted on 1 Aug 2012)
A tensor network formalism of thermofield dynamics is introduced. The formalism relates the original Hilbert space with its tilde space by a product of two copies of a tensor network. Then, their interface becomes an event horizon, and the logarithm of the tensor rank corresponds to the black hole entropy. Eventually, multiscale entanglement renormalization anzats (MERA) reproduces an AdS black hole at finite temperature. Our finding shows rich functionalities of MERA as efficient graphical representation of AdS/CFT correspondence.

http://arxiv.org/abs/1307.1522
Global symmetries in tensor network states: symmetric tensors versus minimal bond dimension
Sukhwinder Singh, Guifre Vidal
(Submitted on 5 Jul 2013)
Tensor networks offer a variational formalism to efficiently represent wave-functions of extended quantum many-body systems on a lattice. In a tensor network N, the dimension \chi of the bond indices that connect its tensors controls the number of variational parameters and associated computational costs. In the absence of any symmetry, the minimal bond dimension \chi^{min} required to represent a given many-body wave-function |\Psi> leads to the most compact, computationally efficient tensor network description of |\Psi>. In the presence of a global, on-site symmetry, one can use a tensor network N_{sym} made of symmetric tensors. Symmetric tensors allow to exactly preserve the symmetry and to target specific quantum numbers, while their sparse structure leads to a compact description and lowers computational costs. In this paper we explore the trade-off between using a tensor network N with minimal bond dimension \chi^{min} and a tensor network N_{sym} made of symmetric tensors, where the minimal bond dimension \chi^{min}_{sym} might be larger than \chi^{min}. We present two technical results. First, we show that in a tree tensor network, which is the most general tensor network without loops, the minimal bond dimension can always be achieved with symmetric tensors, so that \chi^{min}_{sym} = \chi^{min}. Second, we provide explicit examples of tensor networks with loops where replacing tensors with symmetric ones necessarily increases the bond dimension, so that \chi_{sym}^{min} > \chi^{min}. We further argue, however, that in some situations there are important conceptual reasons to prefer a tensor network representation with symmetric tensors (and possibly larger bond dimension) over one with minimal bond dimension.

http://arxiv.org/abs/1307.1604
Can a wormhole be interpreted as an EPR pair?
H. Nikolic
(Submitted on 5 Jul 2013)
Recently, Maldacena and Susskind arXiv:1306.0533 and Jensen and Karch arXiv:1307.1132 argued that a wormhole can be interpreted as an EPR pair. We point out that a convincing justification of such an interpretation would require a quantitative evidence that correlations between two ends of the wormhole are equal to those between the members of the EPR pair. As long as the existing results do not contain such evidence, the interpretation of wormhole as an EPR pair does not seem justified.

 

[atyy]

John Preskill's Entanglement = Wormholes describes the Maldacena-Susskind ER=EPR proposal and, following a note from a commenter JM, mentions Swingle's "beautiful 2009 paper".

This paper has a fascinating result mentions both the Swingle papers and the Bianchi-Myers proposal:

http://arxiv.org/abs/1305.0856
The entropy of a hole in spacetime
Vijay Balasubramanian, Bartlomiej Czech, Borun D. Chowdhury, Jan de Boer
(Submitted on 3 May 2013)
We compute the gravitational entropy of 'spherical Rindler space', a time-dependent, spherically symmetric generalization of ordinary Rindler space, defined with reference to a family of observers traveling along non-parallel, accelerated trajectories. All these observers are causally disconnected from a spherical region H (a 'hole') located at the origin of Minkowski space. The entropy evaluates to S = A/4G, where A is the area of the spherical acceleration horizon, which coincides with the boundary of H. We propose that S is the entropy of entanglement between quantum gravitational degrees of freedom supporting the interior and the exterior of the sphere H.

I'm looking forward to Bianchi's talk at Loops 2013!

 

[atyy]

So if condensed matter systems can implement gauge/gravity duality, could experimentalists settle the firewall debate?

 

[mitchell porter]

Interesting idea. But you would know this topic much better than me... Is there really a good condensed matter analogue for black holes? For holographic black holes? For black hole evaporation? The firewall is only supposed to exist late in the black hole's life, right?

 

[atyy]

Interesting idea. But you would know this topic much better than me... Is there really a good condensed matter analogue for black holes? For holographic black holes? For black hole evaporation? The firewall is only supposed to exist late in the black hole's life, right?

Actually, I don't know the "real life" aspect well. Incidentally, glancing through the new version of the argument from Marolf and Polchinski, there doesn't seem to be a requirement for late time black holes any more - are they now claiming it's totally generic?

 

[atyy]

The Perimeter Institute's adverstising apparatus has an article about its http://www.perimeterinstitute.ca/node/88087. (Not sure I'd like the advertisement if I were a backhoe ...)

Some of the work described involves a collaboration between Dittrich and Martin-Benito, who are LQG folks and Erik Schnetter, who's a computational guy. The paper is Coarse graining of spin net models: dynamics of intertwiners. It's interesting compared to earlier numerical LQG work, because the amplitudes in the new spin foam models are not positive. Tensor networks were developed to overcome this problem in condensed matter physics, making simulations with fermions much more feasible. Now they've applied it to a toy version of LQG. They get the phase diagram of their toy, and also get an interesting new result: "This procedure will also reveal an unexpected fixed point, which turns out to define a new triangulation invariant vertex model."

There's also numerical work on an Ising-like model in Shenker and Stanford's Black holes and the butterfly effect. A closely related paper is Liu and Suh's Entanglement Tsunami.

 

[atyy]

Bianchi and Krasnov both gave very entertaining talks at Loops 13. Bianchi talks about spin foams and briefly mentions tensor product states in the middle of his talk, while Krasnov suggests attempting to quantize diff-invariant gauge theories by putting them on the lattice.

http://pirsa.org/13070048
Entanglement, Bekenstein-Hawking Entropy and Spinfoams
Speaker(s): Eugenio Bianchi
Abstract: I review recent developments on vacuum entanglement perturbations in perturbative quantum gravity and spinfoams, and discuss their relevance for understanding the nature of black hole entropy.
Date: 23/07/2013 - 9:45 am
Collection: Loops 13

http://pirsa.org/13070081/
Diffeomorphism Invariant Gauge Theories
Speaker(s): Kirill Krasnov
Abstract: I will describe a very large class of gauge theories that do not use any external structure such as e.g. a spacetime metric in their construction. When the gauge group is taken to be SL(2) these theories describe interacting gravitons, with GR being just a particular member of a whole family of gravity theories. Taking larger gauge groups one obtains gravity coupled to various matter systems. In particular, I will show how gravity together with Yang-Mills gauge fields arise from one and the same diffeomorphism invariant gauge theory Lagrangian. Finally, I will describe what is known about these theories quantum mechanically.
Date: 26/07/2013 - 9:45 am
Collection: Loops 13

http://arxiv.org/abs/1307.7738
Holography of the BTZ Black Hole, Inside and Out
Anton de la Fuente, Raman Sundrum
(Submitted on 29 Jul 2013)
We propose a CFT dual structure for quantum gravity and matter on the extended BTZ black hole, realized as a quotient of the Poincare patch of AdS3. The CFT is taken to "live" on the BTZ boundary, with components outside the horizon as well as inside the singularity, the latter containing closed timelike curves, and with different components connected by lightlike circles. Much of the paper is concerned with making concrete non-perturbative sense of these (at first sight) troubling features. After some massaging, we arrive at a simple and natural generalization of the thermal density matrix and of thermofield entanglement, to capture probes behind the horizon using specific non-local observables. Our checks include re-deriving all tree-level BTZ bulk and boundary effective field theory correlators, assuming only the standard AdS/CFT duality on the Poincare patch. This is accomplished by reanalyzing the Rindler view of standard AdS/CFT, followed by exploiting the simple quotient structure of BTZ. We study the BTZ singularity in the Poincare patch realization and show that, despite cancelations of divergences in correlators, BTZ effective field theory does break down there. Our CFT dual proposal is however manifestly UV-complete and well-defined, and clarifies the unified nature of the singularity and the horizon.

 

[atyy]

http://arxiv.org/abs/1308.0289
Are entangled particles connected by wormholes? Support for the ER=EPR conjecture from entropy inequalities
Hrant Gharibyan, Robert F. Penna
(Submitted on 1 Aug 2013)
If spacetime is built out of quantum bits, does the shape of space depend on how the bits are entangled? The ER=EPR conjecture relates the entanglement entropy of a collection of black holes to the cross sectional area of Einstein-Rosen (ER) bridges (or wormholes) connecting them. We show that the geometrical entropy of classical ER bridges satisfies the subadditivity, triangle, strong subadditivity, and CLW inequalities. These are nontrivial properties of entanglement entropy, so this is evidence for ER=EPR. We further show that the entanglement entropy associated to classical ER bridges has nonpositive interaction information. This is not a property of entanglement entropy, in general. For example, the entangled four qubit pure state |GHZ_4>=(|0000>+|1111>)/\sqrt{2} has positive interaction information, so this state cannot be described by a classical ER bridge. Large black holes with massive amounts of entanglement between them can fail to have a classical ER bridge if they are built out of |GHZ_4> states. States with nonpositive interaction information are called monogamous. We conclude that classical ER bridges require monogamous EPR correlations.

 

[atyy]

In http://arxiv.org/abs/1211.0522 and http://pirsa.org/13070048 , Eugenio Bianchi argues that black hole entropy may be due to entanglement rather than state counting.

However, that entanglement may produce thermalization in subsystems is an old idea. So perhaps the question is what is the relationship between microcanonical and canonical ensembles in "canonical typicality"?

http://arxiv.org/abs/cond-mat/9403051
Chaos and Quantum Thermalization
Mark Srednicki

http://arxiv.org/abs/cond-mat/0511091
Canonical Typicality
Sheldon Goldstein, Joel L. Lebowitz, Roderich Tumulka, Nino Zanghi

http://arxiv.org/abs/quant-ph/0511225
The foundations of statistical mechanics from entanglement: Individual states vs. averages
Sandu Popescu, Anthony J. Short, Andreas Winter

 

[marcus]

I was just rewatching the talks by Pranzetti and by Haggard which discuss things like the equivalence of von Neumann and Boltzmann entropy and the fact that boundary states are inherently mixed (no clear distinction between statistical and pure states).
Haggard's talk is based on collaboration with Eugenio--he mentions they are currently working on yet another paper. It's a lively area of research.
Pranzetti's is the first talk of the session and Haggard's follows immediately afterward (minute 20):
http://pirsa.org/13070054/
Haggard is talking about a "quantum version of the equivalence principle".

I didn't know of the Popescu et al paper, one that certainly seems relevant! The present work on foundations of statistical mechanics is aimed at a general covariant version. I'll check Popescu et al and see if they are working in a GR context.

EDIT: apparently not. What they call the "universe" (they use quotes) is a large isolated quantum system with definite energy E, distinguished time variable, and zero entropy (they assume we have perfect information about the "universe"). Still interesting though. They cite Yakir Aharonov. (Someone Bianchi has also credited in one or more of his papers. He may have cited Popescu as well, I just don't recall.)

 

[atyy]

I was just rewatching the talks by Pranzetti and by Haggard which discuss things like the equivalence of von Neumann and Boltzmann entropy and the fact that boundary states are inherently mixed (no clear distinction between statistical and pure states).
Haggard's talk is based on collaboration with Eugenio--he mentions they are currently working on yet another paper. It's a lively area of research.
Pranzetti's is the first talk of the session and Haggard's follows immediately afterward (minute 20):
http://pirsa.org/13070054/
Haggard is talking about a "quantum version of the equivalence principle".

Pranzetti's result seems sweet and mysterious - how can the Immirzi parameter be negative? 3 years ago in post #4, Physics Monkey said, "Furthermore, there are some exciting hints relating the way one computes black hole entropy in loop quantum gravity and entanglement entropy in the tensor network approach.". I believe at that time he was thinking primarily of the Ashtekar, Baez, Corichi and Krasnov state counting approach, so he was referring to a relationship between entanglement and state counting. Here's Pranzetti's paper:

http://arxiv.org/abs/1305.6714
Black hole entropy from KMS-states of quantum isolated horizons
Daniele Pranzetti
(Submitted on 29 May 2013)
By reintroducing Lorentz invariance via a complex connection formulation in canonical loop quantum gravity, we define a geometrical notion of temperature for quantum isolated horizons. Upon imposition of the reality conditions in the form of the linear simplicity constraints for an imaginary Barbero-Immirzi parameter, the exact formula for the temperature can be derived by demanding that the horizon state satisfying the boundary conditions be a KMS-state. In this way, our analysis reveals the connection between the passage to the Ashtekar self-dual variables and the thermality of the horizon. The horizon equilibrium state can then be used to compute both the von Neumann and the Boltzmann entropies. By means of a natural cut-off introduced by the topological theory on the boundary, we show that the two provide the same finite answer which allows us to recover the Bekenstein-Hawking formula in the semi-classical limit. The connection with Connes-Rovelli thermal time proposal for a general relativistic statistical mechanics is worked out.

 

[atyy]

http://arxiv.org/abs/1308.2342
Bekenstein-Hawking Entropy as Topological Entanglement Entropy
Lauren McGough, Herman Verlinde
(Submitted on 10 Aug 2013)
Black holes in 2+1 dimensions enjoy long range topological interactions similar to those of non-abelian anyon excitations in a topologically ordered medium. Using this observation, we compute the topological entanglement entropy of BTZ black holes, via the established formula S_top = log(S^a_0), with S_b^a the modular S-matrix of the Virasoro characters chi_a(tau). We find a precise match with the Bekenstein-Hawking entropy. This result adds a new twist to the relationship between quantum entanglement and the interior geometry of black holes. We generalize our result to higher spin black holes, and again find a detailed match. We comment on a possible alternative interpretation of our result in terms of boundary entropy.

 

[Physics Monkey]

Entanglement renormalization and holography, aka tensor networks and gravity, was mentioned in the NY Times yesterday in the context of the firewall debate: http://www.nytimes.com/2013/08/13/s...ped-in-a-firewall-paradox.html?pagewanted=all

The work was also mentioned in an Scientific American article by Sachdev back in January: http://www.scientificamerican.com/article.cfm?id=string-theory-helps-explain-quantum-phases-matter

 

[atyy]

http://arxiv.org/abs/quant-ph/0701002
Can EPR correlations be driven by an effective wormhole?

E. Sergio Santini
(Submitted on 30 Dec 2006)
We consider the two-particle wave function of an EPR system given by a two dimensional relativistic scalar field model. The Bohm-de Broglie interpretation is applied and the quantum potential is viewed as modifying the Minkowski geometry. In such a way singularities appear in the metric, opening the possibility, following Holland, of interpreting the EPR correlations as originated by a wormhole effective geometry, through which physical signals can propagate.

http://arxiv.org/abs/quant-ph/0701106
Might EPR particles communicate through a wormhole?

E. Sergio Santini
(Submitted on 16 Jan 2007 (v1), last revised 24 Mar 2007 (this version, v2))
We consider the two-particle wave function of an Einstein-Podolsky-Rosen system, given by a two dimensional relativistic scalar field model. The Bohm-de Broglie interpretation is applied and the quantum potential is viewed as modifying the Minkowski geometry. In this way an effective metric, which is analogous to a black hole metric in some limited region, is obtained in one case and a particular metric with singularities appears in the other case, opening the possibility, following Holland, of interpreting the EPR correlations as being originated by an effective wormhole geometry, through which the physical signals can propagate.

P. R. Holland,The Quantum Theory of Motion: An Account of the de Broglie-Bohm Causal
Interpretation of Quantum Mechanics (Cambridge University Press, Cambridge, 1993).

 

[marcus]

Another from Physicsmonkey!
http://arxiv.org/abs/1308.3234
Entanglement entropy of compressible holographic matter: loop corrections from bulk fermions
Brian Swingle, Liza Huijse, Subir Sachdev
(Submitted on 14 Aug 2013)
Entanglement entropy is a useful probe of compressible quantum matter because it can detect the existence of Fermi surfaces, both of microscopic fermionic degrees of freedom and of "hidden" gauge charged fermions. Much recent attention has focused on holographic efforts to model strongly interacting compressible matter of interest for condensed matter physics. We complete the entanglement analysis initiated in Huijse et al., Phys. Rev. B 85, 035121 (2012) (arXiv:1112.0573) and Ogawa et al., JHEP 1, 125 (2012) (arXiv:1111.1023) using the recent proposal of Faulkner et al. (arXiv:1307.2892) to analyze the entanglement entropy of the visible fermions which arises from bulk loop corrections. We find perfect agreement between holographic and field theoretic calculations.
10 pages, 4 figures

The key paper built on here is by Faulkner Lewkowycz Maldacena (2013), their reference [34].
Page 2: "Thus our results provide a very clean test of the proposed loop correction in Ref. [34]."

Incidentally they also reference [41] Bianchi Myers (2012) at one point as an earlier paper arguing along similar lines.
Page 3: "More recently still, Ref. [34] argued that the picture of quantum corrections around black hole geometries also generalized to the minimal surface situation. See also Ref. [41] for a similar earlier argument."

 

[atyy]

http://arxiv.org/abs/1301.7449
Emergent Space-time Supersymmetry at the Boundary of a Topological Phase
Tarun Grover, D. N. Sheng, Ashvin Vishwanath
In contrast to ordinary symmetries, supersymmetry interchanges bosons and fermions. Originally proposed as a symmetry of our universe, it still awaits experimental verification. Here we theoretically show that supersymmetry emerges naturally in topological superconductors, which are well-known condensed matter systems. Specifically, we argue that the quantum phase transitions at the boundary of topological superconductors in both two and three dimensions display supersymmetry when probed at long distances and times. Supersymmetry entails several experimental consequences for these systems, such as, exact relations between quantities measured in disparate experiments, and in some cases, exact knowledge of the universal critical exponents. The topological surface states themselves may be interpreted as arising from spontaneously broken supersymmetry, indicating a deep relation between topological phases and SUSY. We discuss prospects for experimental realization in films of superfluid He$_3$-B.

http://arxiv.org/abs/1308.3716
Gravitational Dynamics From Entanglement "Thermodynamics"
Nima Lashkari, Michael B. McDermott, Mark Van Raamsdonk
(Submitted on 16 Aug 2013)
In a general conformal field theory, perturbations to the vacuum state obey the relation \delta S = \delta E, where \delta S is the change in entanglement entropy of an arbitrary ball-shaped region, and \delta E is the change in ``hyperbolic'' energy of this region. In this note, we show that for holographic conformal field theories, this relation, together with the holographic connection between entanglement entropies and areas of extremal surfaces and the standard connection between the field theory stress tensor and the boundary behavior of the metric, implies that geometry dual to the perturbed state satisfies Einstein's equations expanded to linear order about pure AdS. We also provide an explicit formula for the linearized metric in terms of the set of entanglement entropies for ball-shaped regions in arbitrary Lorentz frames, making use of the hyperbolic Radon transform.

http://arxiv.org/abs/1308.3792
Entropic Counterpart of Perturbative Einstein Equation
Jyotirmoy Bhattacharya, Tadashi Takayanagi
(Submitted on 17 Aug 2013)
Entanglement entropy in a field theory, with a holographic dual, may be viewed as a quantity which encodes the diffeomorphism invariant bulk gravity dynamics. This, in particular, indicates that the bulk Einstein equations would imply some constraints for the boundary entanglement entropy. In this paper we focus on the change in entanglement entropy, for small but arbitrary fluctuations about a given state, and analyze the constraints imposed on it by the perturbative Einstein equations, linearized about the corresponding bulk state. Specifically, we consider linear fluctuations about BTZ black hole in 3 dimension, pure AdS and AdS Schwarzschild black holes in 4 dimensions and obtain a diffeomorphism invariant reformulation of linearized Einstein equation in terms of holographic entanglement entropy. We will also show that entanglement entropy for boosted subsystems provides the information about all the components of the metric with a time index.

http://arxiv.org/abs/1308.3695
Holographic EPR Pairs, Wormholes and Radiation
Mariano Chernicoff, Alberto Guijosa, Juan F. Pedraza
(Submitted on 16 Aug 2013)
As evidence for the ER=EPR conjecture, it has recently been observed that the string that is holographically dual to an entangled quark-antiquark pair separating with (asymptotically) uniform acceleration has a wormhole on its worldsheet. We point out that a two-sided horizon and a wormhole actually appear for much more generic quark-antiquark trajectories, which is consistent with the fact that the members of an EPR pair need not be permanently out of causal contact. The feature that determines whether the causal structure of the string worldsheet is trivial or not turns out to be the emission of gluonic radiation by the dual quark and antiquark. In the strongly-coupled gauge theory, it is only when radiation is emitted that one obtains an unambiguous separation of the pair into entangled subsystems, and this is what is reflected on the gravity side by the existence of the worldsheet horizon.

 

[atyy]

Juan Maldacena , Spacetime from Entanglement
http://online.kitp.ucsb.edu/online/fuzzorfire-m13/maldacena/

Fun talk in which Maldacena gives a tutorial on tensor networks.

 

[atyy]

I didn't understand this at all, but here's a legendary condensed matter theorist talking about firewalls and postselection. http://online.kitp.ucsb.edu/online/fuzzorfire_m13/kitaev/

Can anyone translate into common speech?

 

[Physics Monkey]

I'm still digesting this talk, but it seems as if he's trying to sketch a question that could determine the fate of the behind the horizon region.

Near the beginning he mentions a relatively simple model consisting of a spin coupled to the left and right moving sectors of a chiral boson. Then there are two possibilities: either the chiral boson goes on forever or it gets terminated in some kind of scrambling system. A physical version of this setup would be something like quantum Hall system, say a Hall bar, in which at one end of the bar is a qubit and at the other end of the bar is some closed system that scrambles or thermalizes. These two systems would then be connected by the edge states of the Hall bar. Thus one has a model of the mirror at infinity (qubit) interacting with the horizon (scrambler).

However, he doesn't seem to make much more explicit of use of that model and goes back the gravity picture. There he sketches some kind of operator setup in the context of a two-sided black hole (in which perhaps the mirror at infinity degrees of freedom can effectively replace one of the sides?) in which one tries to evaluate an observable (what he calls O) in terms of the initial state and some kind of probe (U).

The conclusion, after some wrangling with the causal structure, seems to be that observable he wants to compute, which is not equivalent to just some unitary evolution and measurement, can be mapped to an observable in post-selected quantum mechanics (which roughly means selecting the subset of measurement outcomes in which the final state has some definite value).

There is some background as well. Preskill mentions in his talk that Kitaev is a fan of the paper http://arxiv.org/abs/hep-th/0310281 which also effectively is using post-selection.

So I think, maybe, Kitaev is trying to argue that some post-selected setup on two copies of the boundary may give information about the behind the horizon region.

Hopefully I can say more later.

 

[ftr]

http://dao.mit.edu/~wen/talks/13TsinghuaClass.pdf

 

[atyy]

http://arxiv.org/abs/1108.3896
Localized qubits in curved spacetimes
Matthew C. Palmer, Maki Takahashi, Hans F. Westman

I found this review by Palmer, Takahashi and Westman to be useful for understanding quantum mechanics in curved spacetime while trying to understand the Horowitz-Maldacena black hole final state model (mentioned by Physics Monkey in #123), and the recent Lloyd-Preskill paper on it, especially as to whether wave function collapse still works. Apparently it's not a problem.

http://dao.mit.edu/~wen/talks/13TsinghuaClass.pdf

Did you attend? The class was probably in English, but it'd be nice to know what "topological order" or "tensor network" are in Chinese

 

[ftr]

Did you attend? The class was probably in English, but it'd be nice to know what "topological order" or "tensor network" are in Chinese

No I didn't, but I did visit all major cities in China last year, very impressive.

"tensor network"=“張網絡”. the characters themselves look like tensor network diagrams

Seriously, what is the claim? are condensed matter approach , loop, holography, ADS/CFT, QFT/curved spacetime or what, all claiming to be right about gravity via entanglement, EPR via gravity/wormhole . In other word are these papers claiming a breakthrough( a conclusion) or they are just saying "hey this looks interesting".

 

[atyy]

No I didn't, but I did visit all major cities in China last year, very impressive.

"tensor network"=“張網絡”. the characters themselves look like tensor network diagrams

Seriously, what is the claim? are condensed matter approach , loop, holography, ADS/CFT, QFT/curved spacetime or what, all claiming to be right about gravity via entanglement, EPR via gravity/wormhole . In other word are these papers claiming a breakthrough( a conclusion) or they are just saying "hey this looks interesting".

Nice! 網絡 is network, but why is tensor 張 ?

The claim is my claim - this looks interesting, let's follow the developments

 

[Physics Monkey]

I have been thinking more about Kitaev's talk. It resonates with an idea I had, although its all rather sketchy.

Roughly speaking, I have the following guess.
1. Spacetime is built from entanglement.
2. Entanglement is a limited resource in the two sided black hole because the dynamics don't couple left and right.
3. The behind the horizon region is associated somehow with entanglement between the two boundaries.
4. However, because the entanglement between these two boundaries is limited (cannot be generated by local operations and classical communication), the part of spacetime associated with the two boundary entanglement should also be limited.
5. Hence the singularity is the system, in effect, running out of entanglement and hence of spacetime.

Making post-selected measurements may be a way to use up different amounts of the entanglement and hence to probe different regions behind the horizon and even the singularity.

 

[atyy]

Physics Monkey, is your idea that the singularity is spacetime running out of entanglement related to the BKL conjecture, which is sometimes stated as spatial points dynamically decoupling near a spacelike singularity? I think Damour, Henneaux and Nicolai suggested that's related to E(10), or something like that. http://arxiv.org/abs/hep-th/0212256

 

[Physics Monkey]

It's an interesting suggestion, I'm not sure.

It would be nice to construct some post-selected measurements (if this is indeed the right way to proceed) that somehow "blow up".

It is curious that in AdS/CFT, say, the fewer the degrees of freedom (e.g. the central charge or N), the larger the curvature in Planck units. So the depletion of degrees of freedom leads to increased curvature.

 

[atyy]

http://arxiv.org/abs/1309.4523
Holography, Entanglement Entropy, and Conformal Field Theories with Boundaries or Defects
Kristan Jensen, Andy O'Bannon
(Submitted on 18 Sep 2013)
We study entanglement entropy (EE) in conformal field theories (CFTs) in Minkowski space with a planar boundary or with a planar defect of any codimension. In any such boundary CFT (BCFT) or defect CFT (DCFT), we consider the reduced density matrix and associated EE obtained by tracing over the degrees of freedom outside of a (hemi-)sphere centered on the boundary or defect. Following Casini, Huerta, and Myers, we map the reduced density matrix to a thermal density matrix of the same theory on hyperbolic space. The EE maps to the thermal entropy of the theory on hyperbolic space. For BCFTs and DCFTs dual holographically to Einstein gravity theories, the thermal entropy is equivalent to the Bekenstein-Hawking entropy of a hyperbolic black brane. We show that the horizon of the hyperbolic black brane coincides with the minimal area surface used in Ryu and Takayanagi's conjecture for the holographic calculation of EE. We thus prove their conjecture in these cases. We use our results to compute the R\'enyi entropies and EE in DCFTs in which the defect corresponds to a probe brane in a holographic dual.

http://arxiv.org/abs/1309.3610
Coarse-grained entropy and causal holographic information in AdS/CFT
William R. Kelly, Aron C. Wall
(Submitted on 14 Sep 2013)
We propose bulk duals for certain coarse-grained entropies of boundary regions. The `one-point entropy' is defined in the conformal field theory by maximizing the entropy in a domain of dependence while fixing the one-point functions. We conjecture that this is dual to the area of the edge of the region causally accessible to the domain of dependence (i.e. the `causal holographic information' of Hubeny and Rangamani). The `future one-point entropy' is defined by generalizing this conjecture to future domains of dependence and their corresponding bulk regions. We show that the future one-point entropy obeys a nontrivial second law. If our conjecture is true, this answers the question "What is the field theory dual of Hawking's area theorem?"

http://arxiv.org/abs/1309.4563
Statistics, holography , and black hole entropy in loop quantum gravity
Amit Ghosh, Karim Noui, Alejandro Perez
(Submitted on 18 Sep 2013)
In loop quantum gravity the quantum states of a black hole horizon are produced by point-like discrete quantum geometry excitations (or punctures) labelled by spin $j$. The excitations possibly carry other internal degrees of freedom also, and the associated quantum states are eigenstates of the area $A$ operator. On the other hand, the appropriately scaled area operator $A/(8\pi\ell)$ is also the physical Hamiltonian associated with the quasilocal stationary observers located at a small distance $\ell$ from the horizon. Thus, the local energy is entirely accounted for by the geometric operator $A$.
We assume that: In a suitable vacuum state with regular energy momentum tensor at and close to the horizon the local temperature measured by stationary observers is the Unruh temperature and the degeneracy of `matter' states is exponential with the area $\exp{(\lambda A/\ell_p^2)}$---this is supported by the well established results of QFT in curved spacetimes, which do not determine $\lambda$ but asserts an exponential behaviour. The geometric excitations of the horizon (punctures) are indistinguishable. In the semiclassical limit the area of the black hole horizon is large in Planck units.
It follows that: Up to quantum corrections, matter degrees of freedom saturate the holographic bound, viz. $\lambda=\frac{1}{4}$. Up to quantum corrections, the statistical black hole entropy coincides with Bekenstein-Hawking entropy $S={A}/({4\ell_p^2})$. The number of horizon punctures goes like $N\propto \sqrt{A/\ell_p^2}$, i.e the number of punctures $N$ remains large in the semiclassical limit. Fluctuations of the horizon area are small while fluctuations of the area of an individual puncture are large. A precise notion of local conformal invariance of the thermal state is recovered in the $A\to\infty$ limit where the near horizon geometry becomes Rindler.

 

[atyy]

http://arxiv.org/abs/1309.6282
Exact holographic mapping and emergent space-time geometry
Xiao-Liang Qi
(Submitted on 24 Sep 2013)
In this paper, we propose an exact holographic mapping which is a unitary mapping from the Hilbert space of a lattice system in flat space (boundary) to that of another lattice system in one higher dimension (bulk). By defining the distance in the bulk system from two-point correlation functions, we obtain an emergent bulk space-time geometry that is determined by the boundary state and the mapping. As a specific example, we study the exact holographic mapping for (1+1)-dimensional lattice Dirac fermions and explore the emergent bulk geometry corresponding to different boundary states including massless and massive states at zero temperature, and the massless system at finite temperature. We also study two entangled one-dimensional chains and show that the corresponding bulk geometry consists of two asymptotic regions connected by a worm-hole. The quantum quench of the coupled chains is mapped to dynamics of the worm-hole. In the end we discuss the general procedure of applying this approach to interacting systems, and other open questions.

This guy is not a string theorist, since he writes 1+1.

 

[atyy]

http://arxiv.org/abs/1309.6935
Probing renormalization group flows using entanglement entropy
Hong Liu, Márk Mezei
(Submitted on 26 Sep 2013)
In this paper we continue the study of renormalized entanglement entropy introduced in [1]. In particular, we investigate its behavior near an IR fixed point using holographic duality. We develop techniques which, for any static holographic geometry, enable us to extract the large radius expansion of the entanglement entropy for a spherical region. We show that for both a sphere and a strip, the approach of the renormalized entanglement entropy to the IR fixed point value contains a contribution that depends on the whole RG trajectory. Such a contribution is dominant, when the leading irrelevant operator is sufficiently irrelevant. For a spherical region such terms can be anticipated from a geometric expansion, while for a strip whether these terms have geometric origins remains to be seen.

 

[atyy]

marcus posted in his bibliography https://www.physicsforums.com/showpost.php?p=4530158&postcount=2042 this new paper by Yasha Neiman.

http://arxiv.org/abs/1310.1839
Action and entanglement in gravity and field theory
Yasha Neiman

"We therefore consider a slight generalization of the Bianchi-Myers conjecture. ... In this paper, we point out that eq. (2) has a classical counterpart in the actions of adjoining spacetime processes."

 

[atyy]

http://arxiv.org/abs/1310.3188
Renormalisation as an inference problem
Cédric Bény, Tobias J. Osborne
(Submitted on 11 Oct 2013)
In physics we attempt to infer the rules governing a system given only the results of imprecise measurements. This is an ill-posed problem because certain features of the system's state cannot be resolved by the measurements. However, by ignoring the irrelevant features, an effective theory can be made for the remaining observable relevant features. We explain how these relevant and irrelevant degrees of freedom can be concretely characterised using quantum distinguishability metrics, thus solving the ill-posed inference problem. This framework then allows us to provide an information-theoretic formulation of the renormalisation group, applicable to both statistical physics and quantum field theory. Using this formulation we argue that, given a natural model for an experimentalist's spatial and field-strength measurement uncertainties, the set of Gaussian states emerges as the relevant manifold of effective states and the n-point correlation functions correspond to the relevant observables. Our methods also provide a way to extend renormalisation techniques to effective models which are not based on the usual quantum field formalism. In particular, we can explain in elementary terms, using the example of a simple classical system, some of the problems occurring in quantum field theory and their solution.

 

[atyy]

http://arxiv.org/abs/1310.4204
A hole-ographic spacetime
Vijay Balasubramanian, Borun D. Chowdhury, Bartlomiej Czech, Jan de Boer, Michal P. Heller
We embed spherical Rindler space -- a geometry with a spherical hole in its center -- in asymptotically AdS spacetime and show that it carries a gravitational entropy proportional to the area of the hole. Spherical AdS-Rindler space is holographically dual to an ultraviolet sector of the boundary field theory given by restriction to a strip of finite duration in time. Because measurements have finite durations, local observers in the field theory can only access information about bounded spatial regions. We propose a notion of Residual Entropy that captures uncertainty about the state of a system left by the collection of local, finite-time observables. For two-dimensional conformal field theories we use holography and the strong subadditivity of entanglement to propose a formula for Residual Entropy and show that it precisely reproduces the areas of circular holes in AdS3. Extending the notion to field theories on strips with variable durations in time, we show more generally that Residual Entropy computes the areas of all closed, inhomogenous curves on a spatial slice of AdS3. We discuss the extension to higher dimensional field theories, the relation of Residual Entropy to entanglement between scales, and some implications for the emergence of space from the RG flow of entangled field theories.

 

[atyy]

marcus started a discussion on Livine's new paper at https://www.physicsforums.com/showthread.php?t=717348

http://arxiv.org/abs/1310.3362
Deformation Operators of Spin Networks and Coarse-Graining
Etera R. Livine

The latest update on Banks and Fischler's Holographic Space-time cites Razvan Gurau's http://arxiv.org/abs/1209.4295 A review of the large N limit of tensor models.

http://arxiv.org/abs/1310.6052
Holographic Space-time and Newton's Law
Tom Banks, Willy Fischler
"There is a large and growing literature on large n tensor models[9] and models with interactions of this type have been studied quite extensively. In the appendix, we give our own derivation of the fact, well known to the cognoscenti, that with a single factor of n^d−3 in the denominator, the interaction would be of order 1 in the large n limit."

I came across Andreas Karch's commentary on Papadodimas and Raju's first paper about firewalls via Lubos Motl's http://motls.blogspot.sg/2013/10/is-space-and-time-emergent-er-epr.html. There are also two new papers elaborating their construction.

http://physics.aps.org/articles/v6/115
Viewpoint: What’s Inside a Black Hole’s Horizon?
Andreas Karch

http://arxiv.org/abs/1310.6334
The Black Hole Interior in AdS/CFT and the Information Paradox
Kyriakos Papadodimas, Suvrat Raju

http://arxiv.org/abs/1310.6335
State-Dependent Bulk-Boundary Maps and Black Hole Complementarity
Kyriakos Papadodimas, Suvrat Raju
Finally, we explore an intriguing link between our construction of interior operators and Tomita-Takesaki theory.

 

[John86]

http://arxiv.org/abs/1309.7011
A new type of nonsingular black-hole solution in general relativity
F.R. Klinkhamer
(Submitted on 26 Sep 2013 (v1), last revised 10 Oct 2013 (this version, v2))
Certain exact solutions of the Einstein field equations over nonsimply-connected manifolds are reviewed. These solutions are spherically symmetric and have no curvature singularity. They can be considered to regularize the Schwarzschild solution with a curvature singularity at the center. Spherically symmetric collapse of matter in R^4 may result in these nonsingular black-hole solutions, if quantum-gravity effects allow for topology change near the center or if the nontrivial topology is already present as a remnant from a quantum spacetime foam.

http://arxiv.org/abs/1309.1845
On the broken time translation symmetry in macroscopic systems: precessing states and off-diagonal long-range order
G.E. Volovik
(Submitted on 7 Sep 2013 (v1), last revised 16 Sep 2013 (this version, v2))
The broken symmetry state with off-diagonal long-range order (ODLRO), which is characterized by the vacuum expectation value of the operator of creation of the conserved quantum number Q, has the time-dependent order parameter. However, the breaking of the time reversal symmetry is observable only if the charge Q is not strictly conserved and may decay. This dihotomy is resolved in systems with quasi-ODLRO. These systems have two well separated relaxation times: the relaxation time \tau_Q of the charge Q and the energy relaxation time \tau_E. If \tau_Q >> \tau_E, the perturbed system relaxes first to the state with the ODLRO, which persists for a long time \tau_Q and finally relaxes to the full equilibrium static state. In the limit \tau_Q -> \infty, but not in the strict limit case when the charge Q is conserved, the intermediate ODLRO state can be considered as the ground state of the system at fixed Q with the observable spontaneously broken time reversal symmetry. Examples of systems with quasi-ODLRO are provided by superfluid phase of liquid 4He, Bose-Einstein condensation of magnons (phase coherent spin precession) and precessing vortices.

http://arxiv.org/abs/1310.3581
Topological matter: graphene and superfluid 3He
M.I. Katsnelson, G.E. Volovik
(Submitted on 14 Oct 2013)
Physics of graphene and physics of superfluid phases of 3He have many common features. Both systems are topological materials where quasiparticles behave as relativistic massless (Majorana or Dirac) fermions. We formulate the points where these features are overlapping. This will allow us to use graphene for study the properties of superfluid 3He, to use superfluid 3He for study the properties of graphene, and to use the combination to study the physics of topological quantum vacuum. We suggest also some particular experiments with superfluid 3He using graphene as an atomically thin membrane impenetrable for He atoms but allowing for momentum and energy transfer.

http://arxiv.org/abs/1310.6295
Kopnin force and chiral anomaly
G.E. Volovik
(Submitted on 23 Oct 2013 (v1), last revised 24 Oct 2013 (this version, v2))
Kopnin spectral flow force acting on quantized vortices in superfluid and superconductors is discussed. Kopnin force represents the first realization of the chiral anomaly in condensed matter.

 

[atyy]

I came across this from Doug Natelson's http://nanoscale.blogspot.sg/2013/10/two-striking-results-on-arxiv.html

http://arxiv.org/abs/1310.5580
How many is different? Answer from ideal Bose gas
Jeong-Hyuck Park
(Submitted on 21 Oct 2013)
How many H2O molecules are needed to form water? While the precise answer is not known, it is clear that the answer should be a finite number rather than infinity. We revisit with care the ideal Bose gas confined in a cubic box which is discussed in most statistical physics textbooks. We show that the isobar of the ideal gas zigzags on the temperature-volume plane featuring a `boiling-like' discrete phase transition, provided the number of particles is equal to or greater than a particular value: 7616. This demonstrates for the first time how a finite system can feature a mathematical singularity and realize the notion of `Emergence', without resorting to the thermodynamic limit.

 

[Physics Monkey]

I came across this from Doug Natelson's http://nanoscale.blogspot.sg/2013/10/two-striking-results-on-arxiv.html

http://arxiv.org/abs/1310.5580
How many is different? Answer from ideal Bose gas
Jeong-Hyuck Park
(Submitted on 21 Oct 2013)
How many H2O molecules are needed to form water? While the precise answer is not known, it is clear that the answer should be a finite number rather than infinity. We revisit with care the ideal Bose gas confined in a cubic box which is discussed in most statistical physics textbooks. We show that the isobar of the ideal gas zigzags on the temperature-volume plane featuring a `boiling-like' discrete phase transition, provided the number of particles is equal to or greater than a particular value: 7616. This demonstrates for the first time how a finite system can feature a mathematical singularity and realize the notion of `Emergence', without resorting to the thermodynamic limit.

I don't understand this paper. For example, why assume the perfect canonical ensemble for so few particles?

 

[atyy]

I don't understand this paper. For example, why assume the perfect canonical ensemble for so few particles?

Did you mean that they should have used the microcanonical ensemble, and the canonical ensemble only makes sense or agrees with the microcanonical in the thermodynamic limit?

 

[Physics Monkey]

That would be one possibility. More generally, why, in an isolated system with no interactions, should I use any thermodynamic ensemble at all? What if the system is in a pure state? Will arbitrarily small interactions change things?

Furthermore, if thermalization is imagined to take place due to interactions with the wall or some bath, the bath-system entanglement might be important. One certainly won't get exactly the state being considered if one traces over the bath.

I also worry about the role of (presumably large) fluctuations in this setup.

I suppose the point is that we do understand very well how phase transitions effectively arise with finite systems and I'm just not sure what I'm supposed to be learning from this calculation. I don't want to be too harsh, I just don't get it.

 

[marcus]

This could be of interest in the context of this thread :
http://arxiv.org/abs/1310.8372
Scaling of entanglement entropy in the (branching) multi-scale entanglement renormalization ansatz
Glen Evenbly, Guifre Vidal
(Submitted on 31 Oct 2013)
We investigate the scaling of entanglement entropy in both the multi-scale entanglement renormalization ansatz (MERA) and in its generalization, the branching MERA. We provide analytical upper bounds for this scaling, which take the general form of a boundary law with various types of multiplicative corrections, including power-law corrections all the way to a bulk law. For several cases of interest, we also provide numerical results that indicate that these upper bounds are saturated to leading order. In particular we establish that, by a suitable choice of holographic tree, the branching MERA can reproduce the logarithmic multiplicative correction of the boundary law observed in Fermi liquids and spin-Bose metals in D≥2 dimensions.
17 pages, 14 figures

 

[atyy]

https://www.physicsforums.com/showpost.php?p=4555721&postcount=9

My pick for the 4th quarter:

http://arxiv.org/abs/1310.7786

Group field theory as the 2nd quantization of Loop Quantum Gravity

Daniele Oriti
(Submitted on 29 Oct 2013)
We construct a 2nd quantized reformulation of canonical Loop Quantum Gravity at both kinematical and dynamical level, in terms of a Fock space of spin networks, and show in full generality that it leads directly to the Group Field Theory formalism. In particular, we show the correspondence between canonical LQG dynamics and GFT dynamics leading to a specific GFT model from any definition of quantum canonical dynamics of spin networks. We exemplify the correspondence of dynamics in the specific example of 3d quantum gravity. The correspondence between canonical LQG and covariant spin foam models is obtained via the GFT definition of the latter.

"The simple but key point of the construction is to realize in which sense LQG states (which we call here generically 'spin network states', even if this name would only strictly apply to LQG states in the spin representation) can be understood as "many-particle" states analogously to those found in particle physics and condensed matter theory."

 

[atyy]

http://arxiv.org/abs/1311.1137
Behind the Horizon in AdS/CFT
Erik Verlinde, Herman Verlinde
(Submitted on 5 Nov 2013)
We extend the recent proposal of Papadodimas and Raju of a CFT construction of operators inside the black hole interior to arbitrary non-maximally mixed states. Our construction builds on the general prescription given in earlier work, based on ideas from quantum error correction. We indicate how the CFT state dependence of the interior modes can be removed by introducing an external system, such as an observer, that is entangled with the CFT.

http://arxiv.org/abs/1311.1784
Topological quasiparticles and the holographic bulk-edge relation in 2+1D string-net models
Tian Lan, Xiao-Gang Wen
(Submitted on 7 Nov 2013)
String-net models allow us to systematically construct and classify 2+1D topologically ordered states which can have gapped boundaries. So we can use the simple ideal string-net wavefunctions to study all the universal properties of such topological orders. In this paper, we describe a finite computational method -- Q-algebra module approach, that allows us to compute the non-Abelian statistics of the topological excitations [described by a modular tensor category (MTC)] from the string-net wavefunction [described by a unitary fusion category (UFC)]: MTC=Z(UFC), where Z is the functor that takes the Drinfeld center. We discuss several examples, including the twisted quantum double Dα(G) phase. Our result can also be viewed from an angle of holographic bulk-boundary relation. The 2+1D topological orders are classified by MTC plus the chiral central charge of the edge states, while the 1+1D anomalous topological orders (that appear on the edge of 2+1D gapped states) are classified by UFC. If we know an edge (described by a UFC) of a gapped 2+1D state, then our method allows us to compute the bulk topological order [described by a MTC=Z(UFC) with zero chiral central charge].

http://arxiv.org/abs/1311.1798
Topological lattice field theories from intertwiner dynamics
Bianca Dittrich, Wojciech Kaminski
(Submitted on 7 Nov 2013)
We introduce a class of 2D lattice models that describe the dynamics of intertwiners, or, in a condensed matter interpretation, the fusion and splitting of anyons. We identify different families and instances of triangulation invariant, that is, topological, models inside this class. These models give examples for symmetry protected topologically ordered 1D quantum phases with quantum group symmetries. Furthermore the models provide realizations for anyon condensation into a new effective vacuum. We explain the relevance of our findings for the problem of identifying the continuum limit of spin foam and spin net models.

 

[atyy]

http://arxiv.org/abs/1311.1643
Volume Law for the Entanglement Entropy in Non-local QFTs
Noburo Shiba, Tadashi Takayanagi
(Submitted on 7 Nov 2013 (v1), last revised 14 Nov 2013 (this version, v2))
In this paper, we present a simple class of non-local field theories whose ground state entanglement entropy follows a volume law as long as the size of subsystem is smaller than a certain scale. We will confirm this volume law both from numerical calculations and from analytical estimation. This behavior fits nicely with holographic results for spacetimes whose curvatures are much smaller than AdS spaces such as those in the flat spacetime.

 

[atyy]

http://arxiv.org/abs/1311.3327
Area law violation for the mutual information in a nonequilibrium steady state
Viktor Eisler, Zoltan Zimboras
(Submitted on 13 Nov 2013)
We study the nonequilibrium steady state of an infinite chain of free fermions, resulting from an initial state where the two sides of the system are prepared at different temperatures. The mutual information is calculated between two adjacent segments of the chain and is found to scale logarithmically in the subsystem size. This provides the first example of the violation of the area law in a quantum many-body system outside a zero temperature regime. The prefactor of the logarithm is obtained analytically and, furthermore, the same prefactor is shown to govern the logarithmic increase of mutual information in time, before the system relaxes locally to the steady state.

 

[atyy]

http://arxiv.org/abs/1311.6095
Holographic Geometry of cMERA for Quantum Quenches and Finite Temperature
Ali Mollabashi, Masahiro Nozaki, Shinsei Ryu, Tadashi Takayanagi
(Submitted on 24 Nov 2013)
We study the time evolution of cMERA (continuous MERA) under quantum quenches in free field theories. We calculate the corresponding holographic metric using the proposal of arXiv:1208.3469 and confirm that it qualitatively agrees with its gravity dual given by a half of the AdS black hole spacetime, argued by Hartman and Maldacena in arXiv:1303.1080. By doubling the cMERA for the quantum quench, we give an explicit construction of finite temperature cMERA. We also study cMERA in the presence of chemical potential and show that there is an enhancement of metric in the infrared region corresponding to the Fermi energy.

 

[marcus]

This Loop paper by Dittrich et al. cites research by B. Swingle and also by G. Vidal. Swingle's paper, for instance, is cited both on page 2 in the introduction and on page 28 of the conclusions [31].
http://arxiv.org/abs/1311.7565
Time evolution as refining, coarse graining and entangling
Bianca Dittrich, Sebastian Steinhaus
(Submitted on 29 Nov 2013)
We argue that refining, coarse graining and entangling operators can be obtained from time evolution operators. This applies in particular to geometric theories, such as spin foams. We point out that this provides a construction principle for the physical vacuum in quantum gravity theories and more generally allows to construct a (cylindrically) consistent continuum limit of the theory.
33 pages, 9 figures

 

[marcus]

Does anyone want to clarify what is going on in this paper?
We point out that this provides a construction principle for the physical vacuum in quantum gravity theories and more generally allows to construct a (cylindrically) consistent continuum limit of the theory.

If that is confirmed applicable in general it would be important: consistent continuum limit! Why should the construction parallel time-evolution?

I've tried reading the paper, but have more than usual difficulty understanding it. There are a bunch of diagrams of Pachner moves that can implement either refinement (in one direction) or coarsegraining (in the other direction). Some other diagrams illustrate moves which produce entanglement. Simpler Pachner move diagrams I don't have trouble reading. It might help if these were redrawn with dotted lines and bold lines giving more hints as to how to read them.

Also I must say I don't grasp the connection with the papers by Swingle and by Vidal, which connection Dittrich considers important enough to emphasize both in the introduction and at the end of the paper in the conclusions.