Condensed matter physics, area laws & LQG?

[atyy]

http://arxiv.org/abs/1508.02538
Hessian geometry and entanglement thermodynamics
Hiroaki Matsueda
(Submitted on 11 Aug 2015)
We reconstruct entanglement thermodynamics by means of Hessian geometry, since this method exactly generalizes thermodynamics into much wider exponential family cases including quantum entanglement. Starting with the correct first law of entanglement thermodynamics, we derive that a proper choice of the Hessian potential leads to both of the entanglement entropy scaling for quantum critical systems and hyperbolic metric (or AdS space with imaginary time). We also derive geometric representation of the entanglement entropy in which the entropy is described as integration of local conserved current of information flowing across an entangling surface. We find that the entangling surface is equivalent to the domain boundary of the Hessian potential. This feature originates in a special property of critical systems in which we can identify the entanglement entropy with the Hessian potential after the second derivative by the canonical parameters, and this identification guarantees violation of extensive nature of the entropy.

 

[atyy]

http://arxiv.org/abs/1508.06572
Quantum information erasure inside black holes
David A. Lowe, Larus Thorlacius
(Submitted on 26 Aug 2015)
An effective field theory for infalling observers in the vicinity of a quasi-static black hole is given in terms of a freely falling lattice discretization. The lattice model successfully reproduces the thermal spectrum of outgoing Hawking radiation, as was shown by Corley and Jacobson, but can also be used to model observations made by a typical low-energy observer who enters the black hole in free fall at a prescribed time. The explicit short distance cutoff ensures that, from the viewpoint of the infalling observer, any quantum information that entered the black hole more than a scrambling time earlier has been erased by the black hole singularity. This property, combined with the requirement that outside observers need at least of order the scrambling time to extract quantum information from the black hole, ensures that a typical infalling observer does not encounter drama upon crossing the black hole horizon in a theory where black hole information is preserved for asymptotic observers.

 

[marcus]

http://arxiv.org/abs/1509.00113
Entanglement Holography
Jan de Boer, Michal P. Heller, Robert C. Myers, Yasha Neiman
(Submitted on 1 Sep 2015)
We demonstrate that for general conformal field theories (CFTs), the entanglement for small perturbations of the vacuum is organized in a novel holographic way. For spherical entangling regions in a constant time slice, perturbations in the entanglement entropy are solutions of a Klein-Gordon equation in an auxiliary de Sitter (dS) spacetime. The role of the emergent time-like direction in dS is played by the size of the entangling sphere. For CFTs with extra conserved charges, e.g., higher spin charges, we show that each charge gives rise to a separate dynamical scalar field in dS.
6 pages, 4 figures

http://arxiv.org/abs/1509.00074
A coarse-grained generalized second law for holographic conformal field theories
William Bunting, Zicao Fu, Donald Marolf
(Submitted on 31 Aug 2015)
We consider the universal sector of a d-dimensional large-N strongly-interacting holographic CFT on a black hole spacetime background B. When our CFT_d is coupled to dynamical Einstein-Hilbert gravity with Newton constant G_d, the combined system can be shown to satisfy a version of the thermodynamic Generalized Second Law (GSL) at leading order in G_d. ...
17 pages, 1 figure

 

[atyy]

http://arxiv.org/abs/1509.02036
A note on quantum supergravity and AdS/CFT
Norbert Bodendorfer
(Submitted on 7 Sep 2015)
We note that the non-perturbative quantisation of supergravity as recently investigated using loop quantum gravity techniques provides an opportunity to probe an interesting sector of the AdS/CFT correspondence, which is usually not considered in conventional treatments. In particular, assuming a certain amount of convergence between the quantum supergravity sector of string theory and quantum supergravity constructed via loop quantum gravity techniques, we argue that the large quantum number expansion in loop quantum supergravity corresponds to the $1/{N_{c}}^2$ expansion in the corresponding gauge theory. In order to argue that we are indeed dealing with an appropriate quantum supergravity sector of string theory, high energy ($α^{′}$) corrections are being neglected, leading to a gauge theory at strong coupling, yet finite $N_{c}$. The arguments given in this paper are mainly of qualitative nature, with the aim of serving as a starting point for a more in depth interaction between the string theory and loop quantum gravity communities.

 

[atyy]

The latest paper by Norbert Bodendorfer http://arxiv.org/abs/1509.02036v1 referenced in post #304 says "The main purpose of this paper is to point out that using techniques from loop quantum gravity [10, 11, 12], a quantisation of supergravity has been constructed [13] which is a good candidate to describe string theory in the appropriate limit corresponding to a strongly coupled gauge theory with a finite number of colours."

Another paper about finite N is Brian Swingle and Mark Van Raamsdonk's http://arxiv.org/abs/1405.2933. Are they talking about the same thing?

 

[atyy]

http://arxiv.org/abs/1510.02103
Holographic RG flows, entanglement entropy and the sum rule
Horacio Casini, Eduardo Teste, Gonzalo Torroba
(Submitted on 7 Oct 2015)
We calculate the two-point function of the trace of the stress tensor in holographic renormalization group flows between pairs of conformal field theories. We show that the term proportional to the momentum squared in this correlator gives the change of the central charge between fixed points in d=2 and in d>2 it gives the holographic entanglement entropy for a planar region. This can also be seen as a holographic realization of the Adler-Zee formula for the renormalization of Newton's constant. Holographic regularization is found to provide a perfect match of the finite and divergent terms of the sum rule, and it is analogous to the regularization of the entropy in terms of mutual information. Finally, we provide a general proof of reflection positivity in terms of stability of the dual bulk action, and discuss the relation between unitarity constraints, the null energy condition and regularity in the interior of the gravity solution.

http://arxiv.org/abs/1510.02367
Bulk Locality from Entanglement in Gauge/Gravity Duality
Jennifer Lin
(Submitted on 8 Oct 2015)
Gauge/gravity duality posits an equivalence between certain strongly coupled quantum field theories and theories of gravity with negative cosmological constant in a higher number of spacetime dimensions. The map between the degrees of freedom on the two sides is non-local and incompletely understood. I describe recent work towards characterizing this map using entanglement in the QFT, where near the dual AdS boundary, the classical energy density at a point in the bulk is stored in the relative entropies of boundary subregions whose homologous minimal surfaces pass through the bulk point. I also derive bulk classical energy conditions near the AdS boundary from entanglement inequalities in the CFT. This is based on the paper [1] with Matilde Marcolli, Hirosi Ooguri and Bogdan Stoica.
More generally, in recent years, there has appeared some evidence that quantum entanglement is responsible for the emergence of spacetime. I review and comment on the state of these developments.

 

[atyy]

http://arxiv.org/abs/1510.04492
An Introduction to Emergent Symmetries
Pedro R. S. Gomes
(Submitted on 15 Oct 2015)
These are intended to be introductory notes on emergent symmetries, i.e., symmetries which manifest themselves in specific sectors of energy in many systems. The emphasis is on the physical aspects rather than computation methods. We include some elementary background material and proceed to our discussion by examining several interesting problems in field theory, statistical mechanics and condensed matter. These problems illustrate how some important symmetries, such as Lorentz invariance and supersymmetry, usually believed to be fundamental, can arise naturally in low-energy regimes of systems involving a large number of degrees of freedom. The aim is to discuss how these examples could help us to face other complex and fundamental problems.

 

[atyy]

http://quantumfrontiers.com/2015/08/16/quantum-information-meets-quantum-matter/
Blog post by Xie Chen: Quantum Information meets Quantum Matter

http://arxiv.org/abs/1508.02595
Quantum Information Meets Quantum Matter -- From Quantum Entanglement to Topological Phase in Many-Body Systems
Bei Zeng, Xie Chen, Duan-Lu Zhou, Xiao-Gang Wen
(Submitted on 11 Aug 2015 (v1), last revised 21 Sep 2015 (this version, v2))
This is the draft version of a textbook, which aims to introduce the quantum information science viewpoints on condensed matter physics to graduate students in physics (or interested researchers). We keep the writing in a self-consistent way, requiring minimum background in quantum information science. Basic knowledge in undergraduate quantum physics and condensed matter physics is assumed. We start slowly from the basic ideas in quantum information theory, but wish to eventually bring the readers to the frontiers of research in condensed matter physics, including topological phases of matter, tensor networks, and symmetry-protected topological phases.

Comments: Hyperref added. This draft is by no means final. Substantial scientific and format changes are still to be made. We have received many helpful comments. We are very grateful for them and will incorporate them into later versions. Please keep sending us comments. The full edition of the book will be available from Springer, in which we will acknowledge the help we have received from everyone

 

[marcus]

335 pages, many figures. check out the table of contents. Doesn't have an alphabetized index yet---something that will make it much easier to use in future.
Wide innovative encompassing vision---XG Wen style. Could become influential. Thanks for spotting this!

 

[democrito]

http://arxiv.org/abs/1510.09020
Entanglement Renormalization and Two Dimensional String Theory
Javier Molina-Vilaplana

The entanglement renormalization flow of a (1+1) free boson is formulated as a path integral over some auxiliary scalar fields. The resulting effective theory for these fields amounts to the dilaton term of non-critical string theory in two spacetime dimensions. A connection between the scalar fields in the two theories is provided, allowing to acquire novel insights into how a theory of gravity emerges from the entanglement structure of another one without gravity.

 

[atyy]

http://arxiv.org/abs/1511.02996
When is an area law not an area law?
Anushya Chandran, Chris Laumann, Rafael D. Sorkin
(Submitted on 10 Nov 2015)
Entanglement entropy is typically proportional to area, but sometimes it acquires an additional logarithmic pre-factor. We offer some intuitive explanations for these facts.

 

[serp777]

http://arxiv.org/abs/1511.02996
When is an area law not an area law?
Anushya Chandran, Chris Laumann, Rafael D. Sorkin
(Submitted on 10 Nov 2015)
Entanglement entropy is typically proportional to area, but sometimes it acquires an additional logarithmic pre-factor. We offer some intuitive explanations for these facts.

Well, to be honest, nothing about entanglement is "intuitive" in my opinion, but maybe its more understandable for people with a physics degree.

 

[atyy]

http://www.nature.com/news/the-quantum-source-of-space-time-1.18797
The quantum source of space-time
Many physicists believe that entanglement is the essence of quantum weirdness — and some now suspect that it may also be the essence of space-time geometry.
Ron Cowen

 

[atyy]

http://arxiv.org/abs/1512.02695
Speed Limits for Entanglement
Thomas Hartman, Nima Afkhami-Jeddi
(Submitted on 8 Dec 2015)
We show that in any relativistic system, entanglement entropy obeys a speed limit set by the entanglement in thermal equilibrium. The bound is derived from inequalities on relative entropy with respect to a thermal reference state. Thus the thermal state constrains far-from-equilibrium entanglement dynamics whether or not the system actually equilibrates, in a manner reminiscent of fluctuation theorems in classical statistical mechanics. A similar shape-dependent bound constrains the full nonlinear time evolution, supporting a simple physical picture for entanglement propagation that has previously been motivated by holographic calculations in conformal field theory. We discuss general quantum field theories in any spacetime dimension, but also derive some results of independent interest for thermal relative entropy in 1+1d CFT.

 

[atyy]

http://arxiv.org/abs/1512.03388
Quantum entanglement in condensed matter systems
Nicolas Laflorencie
(Submitted on 10 Dec 2015)
This review focuses on the field of quantum entanglement applied to condensed matter physics systems with strong correlations, a domain which has rapidly grown over the last decade. By tracing out part of the degrees of freedom of correlated quantum systems, useful and non-trivial informations can be obtained through the study of the reduced density matrix, whose eigenvalue spectrum (the entanglement spectrum) and the associated R\'enyi entropies are now well recognized to contains key features. In particular, the celebrated area law for the entanglement entropy of ground-states will be discussed from the perspective of its subleading corrections which encode universal details of various quantum states of matter, e.g. symmetry breaking states or topological order. Going beyond entropies, the study of the low-lying part of the entanglement spectrum also allows to diagnose topological properties or give a direct access to the excitation spectrum of the edges, and may also raise significant questions about the underlying entanglement Hamiltonian. All these powerful tools can be further applied to shed some light on disordered quantum systems where impurity/disorder can conspire with quantum fluctuations to induce non-trivial effects. Disordered quantum spin systems, the Kondo effect, or the many-body localization problem, which have all been successfully (re)visited through the prism of quantum entanglement, will be discussed in details. Finally, the issue of experimental access to entanglement measurement will be addressed, together with its most recent developments.

 

[atyy]

.Scott started a discussion on an extremely interesting paper in https://www.physicsforums.com/threads/spectral-gap-or-gapless-undecidable.847554/

http://arxiv.org/abs/1502.04135
Undecidability of the Spectral Gap (short version)
Toby Cubitt, David Perez-Garcia, Michael M. Wolf
(Submitted on 13 Feb 2015)
The spectral gap -- the difference in energy between the ground state and the first excited state -- is one of the most important properties of a quantum many-body system. Quantum phase transitions occur when the spectral gap vanishes and the system becomes critical. Much of physics is concerned with understanding the phase diagrams of quantum systems, and some of the most challenging and long-standing open problems in theoretical physics concern the spectral gap, such as the Haldane conjecture that the Heisenberg chain is gapped for integer spin, proving existence of a gapped topological spin liquid phase, or the Yang-Mills gap conjecture (one of the Millennium Prize problems). These problems are all particular cases of the general spectral gap problem: Given a quantum many-body Hamiltonian, is the system it describes gapped or gapless?
Here we show that this problem is undecidable, in the same sense as the Halting Problem was proven to be undecidable by Turing. A consequence of this is that the spectral gap of certain quantum many-body Hamiltonians is not determined by the axioms of mathematics, much as Goedels incompleteness theorem implies that certain theorems are mathematically unprovable. We extend these results to prove undecidability of other low temperature properties, such as correlation functions. The proof hinges on simple quantum many-body models that exhibit highly unusual physics in the thermodynamic limit.

Comments: 8 pages, 3 figures. See long companion paper arXiv:1502.04573 (same title and authors) for full technical details

 

[marcus]

http://arxiv.org/abs/1512.04993
Complexity, Action, and Black Holes
Adam Brown, Daniel A. Roberts, Leonard Susskind, Brian Swingle, Ying Zhao
(Submitted on 15 Dec 2015)
Our earlier paper "Complexity Equals Action" conjectured that the quantum computational complexity of a holographic state is given by the classical action of a region in the bulk (the `Wheeler-DeWitt' patch). We provide calculations for the results quoted in that paper, explain how it fits into a broader (tensor) network of ideas, and elaborate on the hypothesis that black holes are fastest computers in nature.
Comments: 55+14 pages, many figures

 

[atyy]

http://arxiv.org/abs/1512.06206
Finite Entanglement Entropy of Black Holes
Stefano Giaccari, Leonardo Modesto, Leslaw Rachwal, Yiwei Zhu
(Submitted on 19 Dec 2015)
We compute the area term contribution to the black holes' entanglement entropy for a class of local or weakly nonlocal renormalizable gravitational theories coupled to matter. For the case of super-renormalizable theories, we can get a finite conical entropy expressed only in terms of the classical Newton constant either by completing the theory to a finite one in dimensional regularization or by removing the quadratic divergences in the cut-off regularization by the introduction of additional interaction terms. Therefore, our result is independent from the renormalization scheme. We also propose a theory in which the renormalization of the Newton constant is entirely due to the standard model matter, arguing that such a contribution does not give the usual interpretational problems of conical entropy discussed in the literature.

http://arxiv.org/abs/1512.06431
Relative entropy equals bulk relative entropy
Daniel L. Jafferis, Aitor Lewkowycz, Juan Maldacena, S. Josephine Suh
(Submitted on 20 Dec 2015)
We consider the gravity dual of the modular Hamiltonian associated to a general subregion of a boundary theory. We use it to argue that the relative entropy of nearby states is given by the relative entropy in the bulk, to leading order in the bulk gravitational coupling. We also argue that the boundary modular flow is dual to the bulk modular flow in the entanglement wedge, with implications for entanglement wedge reconstruction.

http://arxiv.org/abs/1512.06784
The 1/N expansion method in quantum field theory
H. Sazdjian
(Submitted on 16 Dec 2015)
The motivations of the 1/N expansion method in quantum field theory are explained. The method is first illustrated with the O(N) model of scalar fields. A second example is considered with the two-dimensional Gross-Neveu model of fermion fields with global U(N) and discrete chiral symmetries. The case of QCD is briefly sketched.

 

[atyy]

http://arxiv.org/abs/1601.05416
Bulk Reconstruction in the Entanglement Wedge in AdS/CFT
Xi Dong, Daniel Harlow, Aron C. Wall
(Submitted on 20 Jan 2016)
In this note we prove a simple theorem in quantum information theory, which implies that bulk operators in the Anti-de Sitter / Conformal Field Theory (AdS/CFT) correspondence can be reconstructed as CFT operators in a spatial subregion A, provided that they lie in its entanglement wedge. This is an improvement on existing reconstruction methods, which have at most succeeded in the smaller causal wedge. The proof is a combination of the recent work of Jafferis, Lewkowycz, Maldacena, and Suh on the quantum relative entropy of a CFT subregion with earlier ideas interpreting the correspondence as a quantum error correcting code.

http://arxiv.org/abs/1601.05611
Asymmetric interiors for small black holes
Daniel Kabat, Gilad Lifschytz
(Submitted on 21 Jan 2016)
We develop the representation of infalling observers and bulk fields in the CFT as a way to understand the black hole interior in AdS. We first discuss properties of CFT states which are dual to black holes. Then we show that in the presence of a Killing horizon bulk fields can be decomposed into pieces we call ingoing and outgoing. The ingoing field admits a simple operator representation in the CFT, even inside a small black hole at late times, which leads to a simple CFT description of infalling geodesics. This means classical infalling observers will experience the classical geometry in the interior. The outgoing piece of the field is more subtle. In an eternal two-sided geometry it can be represented as an operator on the left CFT. In a stable one-sided geometry it can be described using entanglement via the PR construction. But in an evaporating black hole trans-horizon entanglement changes at the Page time, which means that for old black holes the PR construction fails and the outgoing field does not see local geometry. This picture of the interior allows the CFT to reconcile unitary Hawking evaporation with the classical experience of infalling observers.

 

[marcus]

http://arxiv.org/abs/1601.05707
Projective quantum states for Loop Quantum Gravity coupled to tensor fields
Andrzej Okolow
(Submitted on 21 Jan 2016)
We present a construction of kinematic quantum states for theories of tensor fields of an arbitrary sort. The construction is based on projective techniques by Kijowski. Applying projective quantum states for Loop Quantum Gravity obtained by Lanery and Thiemann we construct quantum states for LQG coupled to tensor fields.
23 pages.
[Atyy, please let me know if this paper does not fit comfortably in your bibliography and I'll delete it]

 

[marcus]

http://arxiv.org/abs/1602.00106
A Note on Entanglement Entropy, Coherent States and Gravity
Madhavan Varadarajan
(Submitted on 30 Jan 2016)
The entanglement entropy of a free quantum field in a coherent state is independent of its stress energy content. We use this result to highlight the fact that while the Einstein equations for first order variations about a locally maximally symmetric vacuum state of geometry and quantum fields seem to follow from Jacobson's principle of maximal vacuum entanglement entropy, their possible derivation from this principle for the physically relevant case of finite but small variations remains an open issue. We also apply this result to the context of Bianchi's identification, independent of unknown Planck scale physics, of the first order variation of Bekenstein Hawking area with that of vacuum entanglement entropy. We argue that under certain technical assumptions this identification seems not to be extendible to the context of finite but small variations to coherent states. Our particular method of estimation of entanglement entropy variation reveals the existence of certain contributions over and above those appearing in Jacobson's and Bianchi's works. We discuss the sense in which these contributions may be subleading to those already present in these works.
15 pages

http://arxiv.org/abs/1602.03237
Can chaos be observed in quantum gravity?
Bianca Dittrich, Philipp A. Hoehn, Tim A. Koslowski, Mike I. Nelson
(Submitted on 10 Feb 2016)
Full general relativity is almost certainly non-integrable and likely chaotic and therefore almost certainly possesses neither differentiable Dirac observables nor a reduced phase space. It follows that the standard notion of observable has to be extended to include non-differentiable or even discontinuous generalized observables. These cannot carry Poisson-algebraic structures and do not admit a standard quantization. This has deep consequences for a quantum theory of gravity, which we investigate in a simple model for a system with Hamiltonian constraint that fails to be completely integrable. We show that basing the quantization on standard topology precludes a semiclassical limit and can even prohibit any solutions to the quantum constraints. Our proposed solution to this problem is to refine topology such that a complete set of Dirac observables becomes continuous. In the toy model it turns out that a refinement to a polymer-type topology, as e.g. used in loop quantum cosmology, is sufficient. Basing quantization of the toy model on this finer topology, we find a complete set of quantum Dirac observables and a suitable semiclassical limit.
4 pages + references

Atyy, please let me know if including the Dittrich et al here diverges from the main thread topic or if it should for any reason be deleted.

 

[atyy]

Atyy, please let me know if including the Dittrich et al here diverges from the main thread topic or if it should for any reason be deleted.

Everything Dittrich does is relevant to this thread - ok, maybe not brushing her teeth, but I'm sure that could be relevant too

 

[atyy]

http://arxiv.org/abs/1509.04507
The limits of Matrix Product State models
Miguel Navascues, Tamas Vertesi
(Submitted on 15 Sep 2015 (v1), last revised 25 Jan 2016 (this version, v2))
For the past twenty years, Tensor Network States (TNS) have been widely used to model the low energy sector of local Hamiltonians. Their success in doing so has led to the wide-held mantra that TNS of low bond dimension are the `only physical states' of natural condensed matter systems. However, given our experimental limitations to interact with such systems, it is not clear how this conjecture translates into any observable effect. In this Letter we give a first step in this direction by identifying particular operational features pertaining to all Matrix Product States (MPS), the class of TNS used to model non-critical one-dimensional spin chains. By exploiting two surprising structural constraints of MPS, we show how to systematically derive `bond dimension witnesses', or k-local operators whose expectation value allows us to lower bound the bond dimension of the underlying quantum state. We extend some of these results to the ansatz of Projected Entangled Pairs States (PEPS). As a bonus, we use our insight on the structure of MPS to: a) derive some limitations on the use of MPS and PEPS for ground state energy computations; b) show how to decrease the complexity and boost the speed of convergence of the semidefinite programming hierarchies described in [Phys. Rev. Lett. 115, 020501 (2015)] for the characterization of finite-dimensional quantum correlations.
Comments: New title, abstract and numerical results. We still do not acknowledge support from the European Research Council

 

[atyy]

http://arxiv.org/abs/1603.05250
A Holographic Entanglement Entropy Conjecture for General Spacetimes
Fabio Sanches, Sean J. Weinberg
(Submitted on 16 Mar 2016)
We present a natural generalization of holographic entanglement entropy proposals beyond the scope of AdS/CFT by anchoring extremal surfaces to holographic screens. Holographic screens are a natural extension of the AdS boundary to arbitrary spacetimes and are preferred codimension 1 surfaces from the viewpoint of the covariant entropy bound. Screens have a unique preferred foliation into codimension 2 surfaces called leaves. Our proposal is to find the areas of extremal surfaces achored to the boundaries of regions in leaves. We show that the properties of holographic screens are sufficient to prove, under generic conditions, that extremal surfaces anchored in this way always lie within a causal region associated with a given leaf. Within this causal region, a maximin construction similar to that of Wall proves that our proposed quantity satisfies standard properties of entanglement entropy like strong subadditivity. We conjecture that our prescription computes entanglement entropies in quantum states that holographically define arbitrary spacetimes, including those in a cosmological setting with no obvious boundary on which to anchor extremal surfaces.

 

[atyy]

http://arxiv.org/abs/1603.08509
Horizon as Critical Phenomenon
Sung-Sik Lee
(Submitted on 28 Mar 2016)
We show that renormalization group(RG) flow can be viewed as a gradual wave function collapse, where a quantum state associated with the action of field theory evolves toward a final state that describes an IR fixed point. The process of collapse is described by the radial evolution in the dual holographic theory. If the theory is in the same phase as the assumed IR fixed point, the initial state is smoothly projected to the final state. If in a different phase, the initial state undergoes a phase transition which in turn gives rise to a horizon in the bulk geometry. We demonstrate the connection between critical behavior and horizon in an example, by deriving the bulk metrics that emerge in various phases of the U(N) vector model in the large N limit based on the holographic dual constructed from quantum RG. The gapped phase exhibits a geometry that smoothly ends at a finite proper distance in the radial direction. The geometric distance in the radial direction measures a complexity : the depth of RG transformation that is needed to project the generally entangled UV state to a direct product state in the IR. For gapless states, entanglement persistently spreads out to larger length scales, and the initial state can not be projected to the direct product state. The obstruction to smooth projection at charge neutral point manifests itself as the long throat in the anti-de Sitter space. The Poincare horizon at infinity marks the critical point which exhibits a divergent length scale in the spread of entanglement. For the gapless states with non-zero chemical potential, the bulk space becomes the Lifshitz geometry with the dynamical critical exponent two. The identification of horizon as critical point may provide an explanation for the universality of horizon. We also discuss the structure of the bulk tensor network that emerges from the quantum RG.

 

[atyy]

http://arxiv.org/abs/1604.00354
Bit threads and holographic entanglement
Michael Freedman, Matthew Headrick
(Submitted on 1 Apr 2016)
The Ryu-Takayanagi (RT) formula relates the entanglement entropy of a region in a holographic theory to the area of a corresponding bulk minimal surface. Using the max flow-min cut principle, a theorem from network theory, we rewrite the RT formula in a way that does not make reference to the minimal surface. Instead, we invoke the notion of a "flow", defined as a divergenceless norm-bounded vector field, or equivalently a set of Planck-thickness "bit threads". The entanglement entropy of a boundary region is given by the maximum flux out of it of any flow, or equivalently the maximum number of bit threads that can emanate from it. The threads thus represent entanglement between points on the boundary, and naturally implement the holographic principle. As we explain, this new picture clarifies several conceptual puzzles surrounding the RT formula. We give flow-based proofs of strong subadditivity and related properties; unlike the ones based on minimal surfaces, these proofs correspond in a transparent manner to the properties' information-theoretic meanings. We also briefly discuss certain technical advantages that the flows offer over minimal surfaces. In a mathematical appendix, we review the max flow-min cut theorem on networks and on Riemannian manifolds, and prove in the network case that the set of max flows varies Lipshitz continuously in the network parameters.

http://arxiv.org/abs/1604.00388
Dynamics of the Area Law of Entanglement Entropy
Stefan Leichenauer, Mudassir Moosa, Michael Smolkin
(Submitted on 1 Apr 2016)
We study the evolution of the universal area law of entanglement entropy when the Hamiltonian of the system undergoes a time dependent perturbation. In particular, we derive a general formula for the time dependent first order correction to the area law under the assumption that the field theory resides in a vacuum state when a small time-dependent perturbation of a relevant coupling constant is turned on. Using this formula, we carry out explicit calculations in free field theories deformed by a time dependent mass, whereas for a generic QFT we show that the time dependent first order correction is governed by the spectral function defining the two-point correlation function of the trace of the energy-momentum tensor. We also carry out holographic calculations based on the HRT proposal and find qualitative and, in certain cases, quantitative agreement with the field theory calculations.

 

[atyy]

http://arxiv.org/abs/1604.01772
EPR Pairs, Local Projections and Quantum Teleportation in Holography
Tokiro Numasawa, Noburo Shiba, Tadashi Takayanagi, Kento Watanabe
(Submitted on 6 Apr 2016)
In this paper we analyze three quantum operations in two dimensional conformal field theories (CFTs): local projection measurements, creations of partial entanglement between two CFTs, and swapping of subsystems between two CFTs. We also give their holographic duals and study time evolutions of entanglement entropy. By combining these operations, we present an analogue of quantum teleportation between two CFTs and give its holographic realization. We introduce a new quantity to probe tripartite entanglement by using local projection measurement.

 

[atyy]

http://arxiv.org/abs/1605.05751
A Holographic Dual of the Quantum Inequalities
Adam R. Levine
(Submitted on 18 May 2016)
In this note, we establish the 2-D Quantum Inequalities - first proved by Flanagan - for all CFTs with a causal holographic dual. Following the treatment of Kelly $\&$ Wall, we establish that the Boundary Causality Condition in an asymptotic AdS spacetime implies the Quantum Inequalities on the boundary. Our results extend easily to curved spacetime and are stable under deformations of the CFT by relevant operators. We discuss higher dimensional generalizations and possible connections to recent bounds on $a/c$ in 4-D CFTs.

 

[atyy]

http://arxiv.org/abs/1605.06166
Topology and geometry cannot be measured by an operator measurement in quantum gravity
David Berenstein, Alexandra Miller
(Submitted on 19 May 2016)
In the context of LLM geometries, we show that superpositions of classical coherent states of trivial topology can give rise to new classical limits where the topology of spacetime has changed. We argue that this phenomenon implies that neither the topology nor the geometry of spacetime can be the result of an operator measurement. We address how to reconcile these statements with the usual semiclassical analysis of low energy effective field theory for gravity.

 

[atyy]

http://arxiv.org/abs/1605.09396
Entanglement Entropy and Duality
Djordje Radicevic
(Submitted on 30 May 2016)
Using the algebraic approach to entanglement entropy, we study several dual pairs of lattice theories and show how the entropy is completely preserved across each duality. Our main result is that a maximal algebra of observables in a region typically dualizes to a non-maximal algebra in a dual region. In particular, we show how the usual notion of tracing out external degrees of freedom dualizes to a tracing out coupled to an additional summation over superselection sectors. We briefly comment on possible extensions of our results to more intricate dualities, including holographic ones.