Condensed matter physics, area laws & LQG?

[marcus]

An intriguing one is Xie Chen's "'Gauging' time reversal symmetry in tensor network states". What?

She was a postdoc for 2 years at Berkeley in Ashvin Vishwanath's group:
https://sites.google.com/site/ashvinvish/Home/people
and in July 2014 moved to Caltech to take a faculty position. Bright young person in what seems like a good field of research to be in. A kind of combination of Quantum Information theory and Condensed Matter?
Here's a Caltech blurb about her joining the faculty
http://www.caltech.edu/news/quantum-information-meets-condensed-matter-inside-mind-xie-chen-43439
She got her PhD at MIT, I vaguely remember her co-authoring with Xiao-Gang Wen, maybe he was her advisor.

 

[atyy]

At the end of his talk, Physics Monkey argues that one can actually get the nonlinear Einstein equations (he just mentions it without much detail, the talk is mainly about the linearized equation). I think so far the published papers only say how to get the linearized Einstein equations, so that should be an interesting paper to wait for.

 

[marcus]

At the end of his talk, Physics Monkey argues that one can actually get the nonlinear Einstein equations (he just mentions it without much detail, the talk is mainly about the linearized equation). I think so far the published papers only say how to get the linearized Einstein equations, so that should be an interesting paper to wait for.

You already gave the link to Physics Monkey's talk, but we've turned a page so I'll bring it forward:
http://simons.berkeley.edu/talks/brian-swingle-2014-04-22
Einstein's Equations Starting from Qubits
Brian Swingle, Harvard University

I was not aware of published papers deriving linearized GR, so one of us should probably post links here as a convenience for anyone who wants to check out what versions of Einstein's equations are being derived from what. It's all pretty interesting! You may recall the LQG paper by Chirco et al which derives the full non-linear Einstein GR equation from quantum gravity degrees of freedom---by showing that it can indeed be viewed as a thermodynamic equation of state (as Jacobson already proved in 1995), but of specific microscopic QG (rather than unknown "hidden" variables, as Jacobson originally suggested).
http://arxiv.org/abs/1401.5262
Spacetime thermodynamics without hidden degrees of freedom
Goffredo Chirco, Hal M. Haggard, Aldo Riello, Carlo Rovelli
(Submitted on 21 Jan 2014)
A celebrated result by Jacobson is the derivation of Einstein's equations from Unruh's temperature, the Bekenstein-Hawking entropy and the Clausius relation. This has been repeatedly taken as evidence for an interpretation of Einstein's equations as equations of state for unknown degrees of freedom underlying the metric. We show that a different interpretation of Jacobson result is possible, which does not imply the existence of additional degrees of freedom, and follows only from the quantum properties of gravity. We introduce the notion of quantum gravitational Hadamard states, which give rise to the full local thermodynamics of gravity.
12 pages, 1 figure

 

[atyy]

http://arxiv.org/abs/1412.0687
Entanglement entropy in three dimensional gravity
Henry Maxfield
(Submitted on 1 Dec 2014)
The Ryu-Takayanagi and covariant Hubeny-Rangamani-Takayanagi proposals relate entanglement entropy in CFTs with holographic duals to the areas of minimal or extremal surfaces in the bulk geometry. We show how, in three dimensional pure gravity, the relevant regulated geodesic lengths can be obtained by writing a spacetime as a quotients of AdS3, with the problem reduced to a simple purely algebraic calculation. We explain how this works in both Lorentzian and Euclidean formalisms, before illustrating its use to obtain novel results in a number of examples, including rotating BTZ, the RP2 geon, and several wormhole geometries. This includes spatial and temporal dependence of single-interval entanglement entropy, despite these symmetries being broken only behind an event horizon. We also discuss considerations allowing HRT to be derived from analytic continuation of Euclidean computations in certain contexts, and a related class of complexified extremal surfaces.

 

[atyy]

http://arxiv.org/abs/1412.1879
Tomography from Entanglement
Jennifer Lin, Matilde Marcolli, Hirosi Ooguri, Bogdan Stoica
(Submitted on 5 Dec 2014)
The Ryu-Takayanagi formula relates the entanglement entropy in a conformal field theory to the area of a minimal surface in its holographic dual. We show that this relation can be inverted for any state in the conformal field theory to compute the bulk stress-energy tensor near the boundary of the bulk spacetime, reconstructing the local data in the bulk from the entanglement on the boundary. We also show that positivity, monotonicity, and convexity of the relative entropy for small spherical domains between the reduced density matrices of any state and of the ground state of the conformal field theory, follow from positivity conditions on the bulk matter energy density. We discuss an information theoretical interpretation of the convexity in terms of the Fisher metric.

http://arxiv.org/abs/1412.1895
Entanglement entropy of electromagnetic edge modes
William Donnelly, Aron C. Wall
(Submitted on 5 Dec 2014)
The vacuum entanglement entropy of Maxwell theory, when evaluated by standard methods, contains an unexpected term with no known statistical interpretation. We resolve this two-decades old puzzle by showing that this term is the entanglement entropy of edge modes: classical solutions determined by the electric field normal to the entangling surface. We explain how the heat kernel regularization applied to this term leads to the negative divergent expression found by Kabat. This calculation also resolves a recent puzzle concerning the logarithmic divergences of gauge fields in 3+1 dimensions.

 

[atyy]

http://arxiv.org/abs/1412.4220
Analog Systems for Gravity Duals
S. Hossenfelder
(Submitted on 13 Dec 2014)
We show that analog gravity systems exist for charged, planar black holes in asymptotic Anti-de Sitter space. These black holes have been employed to describe, via the gauge-gravity duality, strongly coupled condensed matter systems on the boundary of AdS-space. The analog gravity system is a different condensed matter system that, in a suitable limit, describes the same bulk physics as the theory on the AdS boundary. This combination of the gauge-gravity duality and analog gravity therefore suggests a duality between different condensed matter systems.

 

[atyy]

http://arxiv.org/abs/1412.8483
ER=EPR, GHZ, and the Consistency of Quantum Measurements
Leonard Susskind
(Submitted on 29 Dec 2014)
This paper illustrates various aspects of the ER=EPR conjecture.It begins with a brief heuristic argument, using the Ryu-Takayanagi correspondence, for why entanglement between black holes implies the existence of Einstein-Rosen bridges.
The main part of the paper addresses a fundamental question: Is ER=EPR consistent with the standard postulates of quantum mechanics? Naively it seems to lead to an inconsistency between observations made on entangled systems by different observers. The resolution of the paradox lies in the properties of multiple black holes, entangled in the Greenberger-Horne-Zeilinger pattern.
The last part of the paper is about entanglement as a resource for quantum communication. ER=EPR provides a way to visualize protocols like quantum teleportation. In some sense teleportation takes place through the wormhole, but as usual, classical communication is necessary to complete the protocol.

 

[marcus]

http://arxiv.org/abs/1501.00003
Holographic entanglement entropy and the internal space
Andreas Karch, Christoph F. Uhlemann
(Submitted on 30 Dec 2014)
We elaborate on the role of extremal surfaces probing the internal space in AdS/CFT. Extremal surfaces in AdS quantify the "geometric" entanglement between different regions in physical space for the dual CFT. This, however, is just one of many ways to split a given system into subsectors, and extremal surfaces in the internal space should similarly quantify entanglement between subsectors of the theory. For the case of AdS₅×S⁵, their area was interpreted as entanglement entropy between U(n) and U(m) subsectors of U(n+m) N=4 SYM. Making this proposal precise is subtle for a number of reasons, the most obvious being that from the bulk one usually has access to gauge-invariant quantities only, while a split into subgroups is inherently gauge variant. We study N=4 SYM on the Coulomb branch, where some of the issues can be mitigated and the proposal can be sharpened. Continuing back to the original AdS₅×S⁵ geometry, we obtain a modified proposal, based on the relation of the internal space to the R-symmetry group.
11 pages, 6 figures

 

[atyy]

http://arxiv.org/abs/1501.00007
The AdS/CFT Correspondence
Veronika E. Hubeny
(Submitted on 30 Dec 2014)
We give a brief review of the AdS/CFT correspondence, which posits the equivalence between a certain gravitational theory and a lower-dimensional non-gravitational one. This remarkable duality, formulated in 1997, has sparked a vigorous research program which has gained in breadth over the years, with applications to many aspects of theoretical (and even experimental) physics, not least to general relativity and quantum gravity. To put the AdS/CFT correspondence in historical context, we start by reviewing the relevant aspects of string theory (of which no prior knowledge is assumed). We then develop the statement of the correspondence, and explain how the two sides of the duality map into each other. Finally, we discuss the implications and applications of the correspondence, and indicate some of the current trends in this subject. The presentation attempts to convey the main concepts in a simple and self-contained manner, relegating supplementary remarks to footnotes.

 

[marcus]

http://arxiv.org/abs/1501.01408
Quantum Gravity as an Information Network: Self-Organization of a 4D Universe
Carlo A. Trugenberger
(Submitted on 7 Jan 2015)
I propose a quantum gravity model in which the fundamental degrees of freedom are pure information bits. The Hamiltonian is a very simple network model consisting of a ferromagnetic Ising model for space-time vertices and an antiferromagnetic Ising model for the links between them. As a result of the frustration arising between these two terms, the ground state self-organizes as a new type of low-clustering, lattice-like graph with finite Hausdorff dimension. The model has three quantum phases: a mean field phase in which the spectral and Hausdorff dimensions coincide and are larger then 4. A fluctuations-dominated phase in which the Hausdorff dimension can only be 4 and the spectral dimension is lower than the Hausdorff dimension and a disordered phase in which there is no space-time interpretation. The large-scale dimension 4 of the universe is related to the upper critical dimension 4 of the Ising model. An ultraviolet fixed point at the lower critical dimension of the Ising model is conjectured to imply the absence of space-time at very small scales. At finite temperatures the universe emerges without big bang and without singularities from a ferromagnetic phase transition in which space-time itself forms out of a hot soup of information bits. When the temperature is lowered the universe unfolds by lowering its connectivity, a mechanism I have called topological expansion. Topological expansion is associated with one emerging dimension describing the unfolding process. Quantum fluctuations about this semiclassical universes are elementary black holes and wormholes. The model admits, however, also macroscopic black hole configurations corresponding to graphs containing holes with no space time inside and around which there are Schwarzschild-like horizons with a lower spectral dimension and an entropy proportional to their area.
12 pages, several tables.
[Atyy let me know if this paper does not fit in with the theme and direction of your bibliography. I will of course be happy to remove it.]

 

[atyy]

http://arxiv.org/abs/1501.05573
Typical Event Horizons in AdS/CFT
Steven G. Avery, David A. Lowe
(Submitted on 22 Jan 2015)
We consider the construction of local bulk operators in a black hole background dual to a pure state in conformal field theory. The properties of these operators in a microcanonical ensemble are studied. It has been argued in the literature that typical states in such an ensemble contain firewalls, or otherwise singular horizons. We argue this conclusion can be avoided with a proper definition of the interior operators.

 

[atyy]

Posted by marcus in his bibliography https://www.physicsforums.com/threa...y-rovellis-program.7245/page-116#post-5037393

http://arxiv.org/abs/1503.02981
Four-Dimensional Entropy from Three-Dimensional Gravity
S. Carlip
(Submitted on 10 Mar 2015)
At the horizon of a black hole, the action of (3+1)-dimensional loop quantum gravity acquires a boundary term that is formally identical to an action for three-dimensional gravity. I show how to use this correspondence to obtain the entropy of the (3+1)-dimensional black hole from well-understood conformal field theory computations of the entropy in (2+1)-dimensional de Sitter space.
8 pages

 

[atyy]

http://arxiv.org/abs/1503.03542
Surface/State Correspondence as a Generalized Holography
Masamichi Miyaji, Tadashi Takayanagi
(Submitted on 12 Mar 2015)
We propose a new duality relation between codimension two space-like surfaces in gravitational theories and quantum states in dual Hilbert spaces. This surface/state correspondence largely generalizes the idea of holography such that we do not need to rely on any existence of boundaries in gravitational spacetimes. The present idea is motivated by the recent interpretation of AdS/CFT in terms of the tensor networks so called MERA. Moreover, we study this correspondence from the viewpoint of entanglement entropy and information metric. The Cramer-Rao bound in quantum estimation theory implies that the quantum fluctuations of radial coordinate of the AdS is highly suppressed in the large N limit.

 

[atyy]

http://arxiv.org/abs/1503.04857
Entanglement entropy converges to classical entropy around periodic orbits
Curtis T. Asplund, David Berenstein
(Submitted on 16 Mar 2015)
We consider oscillators evolving subject to a periodic driving force that dynamically entangles them, and argue that this gives the linearized evolution around periodic orbits in a general chaotic Hamiltonian dynamical system. We show that the entanglement entropy, after tracing over half of the oscillators, generically asymptotes to linear growth at a rate given by the sum of the positive Lyapunov exponents of the system. These exponents give a classical entropy growth rate, in the sense of Kolmogorov, Sinai and Pesin. We also calculate the dependence of this entropy on linear mixtures of the oscillator Hilbert space factors, to investigate the dependence of the entanglement entropy on the choice of coarse-graining. We find that for almost all choices the asymptotic growth rate is the same.

 

[atyy]

http://arxiv.org/abs/1502.05385
Tensor network renormalization yields the multi-scale entanglement renormalization ansatz
Glen Evenbly, Guifre Vidal
(Submitted on 18 Feb 2015)
We show how to build a multi-scale entanglement renormalization ansatz (MERA) representation of the ground state of a many-body Hamiltonian H by applying the recently proposed \textit{tensor network renormalization} (TNR) [G. Evenbly and G. Vidal, arXiv:1412.0732] to the Euclidean time evolution operator e−βH for infinite β. This approach bypasses the costly energy minimization of previous MERA algorithms and, when applied to finite inverse temperature β, produces a MERA representation of a thermal Gibbs state. Our construction endows TNR with a renormalization group flow in the space of wave-functions and Hamiltonians (and not just in the more abstract space of tensors) and extends the MERA formalism to classical statistical systems.

Evenbly and Vidal make a comment on ER=EPR in the section on thermal MERA.

 

[Jimster41]

Nice one to dig into. lots of pictures. I found the paragraph I think you mean, and I can at least follow the structure of what they are talking about.

I am missing the quantum-BH relationship. I have a hard time getting anything from the association. I can only surmise that it makes sense to view the quantum "Ket" as an interface to a BH? In the case of the infinite strip, as a "space-like-cross-section of BH space-time geometry" If "BH" wasn't in the sentence, I would think i was following.

Ah, I found the brief wiki on Planck scale black hole entanglement. Very helpful. Yeah, now I do think I'm following...

 

[atyy]

http://arxiv.org/abs/1503.07699
Information Geometry of Entanglement Renormalization for free Quantum Fields
Javier Molina-Vilaplana
(Submitted on 26 Mar 2015)
We provide an explicit connection between the differential generation of entanglement entropy in a tensor network representation of the ground states of two field theories, and a geometric description of these states based on the Fisher information metric. We show how the geometrical description remains invariant despite there is an irreducible gauge freedom in the definition of the tensor network. The results might help to understand how spacetimes may emerge from distributions of quantum states, or more concretely, from the structure of the quantum entanglement concomitant to those distributions.

 

[atyy]

Nice one to dig into. lots of pictures. I found the paragraph I think you mean, and I can at least follow the structure of what they are talking about.

I am missing the quantum-BH relationship. I have a hard time getting anything from the association. I can only surmise that it makes sense to view the quantum "Ket" as an interface to a BH? In the case of the infinite strip, as a "space-like-cross-section of BH space-time geometry" If "BH" wasn't in the sentence, I would think i was following.

Ah, I found the brief wiki on Planck scale black hole entanglement. Very helpful. Yeah, now I do think I'm following...

I think the black hole geometry idea is related to the speculative paper of Hartmann and Maldacena http://arxiv.org/abs/1303.1080, in which they argue for the tensor network in their Fig. 11 to be a coarse representation of a black hole. Evenbly and Vidal's http://arxiv.org/abs/1502.05385 Fig. 2b looks similar, which I think is why they argue that it's related to a black hole. The whole thing is based on Maldacena's proposal that the thermofield double represents a black hole, which recently developed into ER=EPR http://arxiv.org/abs/1306.0533 by Susskind and Maldacena.

 

[Jimster41]

Thanks for those references. I can see it is a whole mountain, with probably a great view. Just starting Susskind's QM Theoretical Min book, so... timely and motivational.

 

[atyy]

At 6:00 in the second of the ER=EPR videos two posts up, Susskind says, "Lampros, if you figure it out and explain it to me, please speak loudly"

So I looked to see who Lampros was, and he's written this interesting paper with Bartlomiej Czech!

http://arxiv.org/abs/1409.4473
Nuts and Bolts for Creating Space
Bartlomiej Czech, Lampros Lamprou
(Submitted on 16 Sep 2014)
We discuss the way in which field theory quantities assemble the spatial geometry of three-dimensional anti-de Sitter space (AdS3). The field theory ingredients are the entanglement entropies of boundary intervals. A point in AdS3 corresponds to a collection of boundary intervals, which is selected by a variational principle we discuss. Coordinates in AdS3 are integration constants of the resulting equation of motion. We propose a distance function for this collection of points, which obeys the triangle inequality as a consequence of the strong subadditivity of entropy. Our construction correctly reproduces the static slice of AdS3 and the Ryu-Takayanagi relation between geodesics and entanglement entropies. We discuss how these results extend to quotients of AdS3 -- the conical defect and the BTZ geometries. In these cases, the set of entanglement entropies must be supplemented by other field theory quantities, which can carry the information about lengths of non-minimal geodesics.

 

[Lord Crc]

Thanks for posting the ER = EPR videos, they were very interesting and easy to follow for a layman like me. lt's hard not to join in on his sense that we are skirting some big breakthough in the near future. Exciting times in any case.

 

[atyy]

Thanks for posting the ER = EPR videos, they were very interesting and easy to follow for a layman like me. lt's hard not to join in on his sense that we are skirting some big breakthough in the near future. Exciting times in any case.

Perhaps it will be a big breakthrough by steady progress, like the computer revolution. Of course they needed the big breakthrough of the transistor, but after that it was a revolution by increments. Here the transistor would be Maldacena's AdS/CFT. Anyway, exciting times indeed.

 

[atyy]

http://arxiv.org/abs/1503.08825
Comments on the Necessity and Implications of State-Dependence in the Black Hole Interior
Kyriakos Papadodimas, Suvrat Raju
(Submitted on 30 Mar 2015)
We revisit the "state-dependence" of the map that we proposed recently between bulk operators in the interior of a large AdS black hole and operators in the boundary CFT. By refining recent versions of the information paradox, we show that this feature is necessary for the CFT to successfully describe local physics behind the horizon --- not only for single-sided black holes but even in the eternal black hole. We show that state-dependence is invisible to an infalling observer who cannot differentiate these operators from those of ordinary quantum effective field theory. Therefore the infalling observer does not observe any violations of quantum mechanics. We successfully resolve a large class of potential ambiguities in our construction. We analyze states where the CFT is entangled with another system and show that the ER=EPR conjecture emerges from our construction in a natural and precise form. We comment on the possible semi-classical origins of state-dependence.

Also mitchell porter started a thread on these interesting papers. Discussion at https://www.physicsforums.com/threads/pentagons-hexagons-quantum-gravity-ads-cft.806003/.

http://arxiv.org/abs/1411.7041
Bulk Locality and Quantum Error Correction in AdS/CFT
Ahmed Almheiri, Xi Dong, Daniel Harlow
(Submitted on 25 Nov 2014 (v1), last revised 21 Feb 2015 (this version, v2))
We point out a connection between the emergence of bulk locality in AdS/CFT and the theory of quantum error correction. Bulk notions such as Bogoliubov transformations, location in the radial direction, and the holographic entropy bound all have natural CFT interpretations in the language of quantum error correction. We also show that the question of whether bulk operator reconstruction works only in the causal wedge or all the way to the extremal surface is related to the question of whether or not the quantum error correcting code realized by AdS/CFT is also a "quantum secret sharing scheme", and suggest a tensor network calculation that may settle the issue. Interestingly, the version of quantum error correction which is best suited to our analysis is the somewhat nonstandard "operator algebra quantum error correction" of Beny, Kempf, and Kribs. Our proposal gives a precise formulation of the idea of "subregion-subregion" duality in AdS/CFT, and clarifies the limits of its validity.

http://arxiv.org/abs/1503.06237
Holographic quantum error-correcting codes: Toy models for the bulk/boundary correspondence
Fernando Pastawski, Beni Yoshida, Daniel Harlow, John Preskill
(Submitted on 20 Mar 2015)
We propose a family of exactly solvable toy models for the AdS/CFT correspondence based on a novel construction of quantum error-correcting codes with a tensor network structure. Our building block is a special type of tensor with maximal entanglement along any bipartition, which gives rise to an exact isometry from bulk operators to boundary operators. The entire tensor network is a quantum error-correcting code, where the bulk and boundary degrees of freedom may be identified as logical and physical degrees of freedom respectively. These models capture key features of entanglement in the AdS/CFT correspondence; in particular, the Ryu-Takayanagi formula and the negativity of tripartite information are obeyed exactly in many cases. That bulk logical operators can be represented on multiple boundary regions mimics the Rindler-wedge reconstruction of boundary operators from bulk operators, realizing explicitly the quantum error-correcting features of AdS/CFT recently proposed by Almheiri et. al in arXiv:1411.7041.

 

[Jimster41]

Staring at sheet of future space two adjacent regions, entangled. Inside them I guess, lies nearly infinite potential complexity. Our history bites the options off, how many qubits at a time?

And what's up with the GHZ state? Are there only triplet GHZ states?

Just got a chance to watch the second one. My head is spinning.

 

[Jimster41]

This woke me up...
Seems pretty topical, esp after listening to Susskind's lecture (I now get more where Condensed Matter Physics comes into this discussion). It just felt pretty concrete after reading in as far as I could...

I found it searching for Ryu Takayanagi... which seems like foundation of what Susskind and his student(s) are talking about, and for which there isn't much on wiki.

http://arxiv.org/abs/1203.4565
The quantum phases of matter
Authors: Subir Sachdev
(Submitted on 20 Mar 2012 (v1), last revised 22 May 2012 (this version, v4))
Abstract: I present a selective survey of the phases of quantum matter with varieties of many-particle quantum entanglement. I classify the phases as gapped, conformal, or compressible quantum matter. Gapped quantum matter is illustrated by a simple discussion of the Z_2 spin liquid, and connections are made to topological field theories. I discuss how conformal matter is realized at quantum critical points of realistic lattice models, and make connections to a number of experimental systems. Recent progress in our understanding of compressible quantum phases which are not Fermi liquids is summarized. Finally, I discuss how the strongly-coupled phases of quantum matter may be described by gauge-gravity duality. The structure of the large N limit of SU(N) gauge theory, coupled to adjoint fermion matter at non-zero density, suggests aspects of gravitational duals of compressible quantum matter.I'd sure love to understand better what they mean when they call the "vision" of the Z2 RVB state, "Dark Matter". I take it they are only being literal - in that it has neither charge nor spin, only energy.

And just in general what a "gapped quantum state" is. I have a cartoon that there is some sort of "entanglement" resonance that changes the Energy Level of the ground state for some quantum ensemble.

Seems relevant, but more trying to calculate causal relationships despite the weirdness (complexity) the the many body quantum lattice state space...
http://arxiv.org/abs/1305.2176

Elementary excitations in gapped quantum spin systems
Jutho Haegeman, Spyridon Michalakis, Bruno Nachtergaele, Tobias J. Osborne, Norbert Schuch, Frank Verstraete
(Submitted on 9 May 2013 (v1), last revised 13 Jun 2013 (this version, v2))
For quantum lattice systems with local interactions, the Lieb-Robinson bound acts as an alternative for the strict causality of relativistic systems and allows to prove many interesting results, in particular when the energy spectrum exhibits an energy gap. In this Letter, we show that for translation invariant systems, simultaneous eigenstates of energy and momentum with an eigenvalue that is separated from the rest of the spectrum in that momentum sector, can be arbitrarily well approximated by building a momentum superposition of a local operator acting on the ground state. The error decreases in the size of the support of the local operator, with a rate that is set by the gap below and above the targeted eigenvalue. We show this explicitly for the AKLT model and discuss generalizations and applications of our result.

 

[atyy]

http://motls.blogspot.com/2015/05/adsmera-tensor-networks-and-string.html
AdS/MERA, tensor networks, and string theory
Lubos Motl

http://www.preposterousuniverse.com/blog/2015/05/05/does-spacetime-emerge-from-quantum-information/
Does Spacetime Emerge From Quantum Information?
Sean Carroll

https://www.quantamagazine.org/20150428-how-quantum-pairs-stitch-space-time/
The Quantum Fabric of Space-Time
Jennifer Ouellette
"Brian Swingle was a graduate student studying the physics of matter at the Massachusetts Institute of Technology when he decided to take a few classes in string theory to round out his education — “because, why not?” he recalled — although he initially paid little heed to the concepts he encountered in those classes. But as he delved deeper, he began to see unexpected similarities between his own work, in which he used so-called tensor networks to predict the properties of exotic materials, and string theory’s approach to black-hole physics and quantum gravity. “I realized there was something profound going on,” he said. ..."

Jennifer Ouellette's article also has a really cute video by Natalie Wolchover of Physics Monkey talking about heavy and light balls falling at the same rate.

http://arxiv.org/abs/1504.06632
Consistency Conditions for an AdS/MERA Correspondence
Ning Bao, ChunJun Cao, Sean M. Carroll, Aidan Chatwin-Davies, Nicholas Hunter-Jones, Jason Pollack, Grant N. Remmen
(Submitted on 24 Apr 2015)
The Multi-scale Entanglement Renormalization Ansatz (MERA) is a tensor network that provides an efficient way of variationally estimating the ground state of a critical quantum system. The network geometry resembles a discretization of spatial slices of an AdS spacetime and "geodesics" in the MERA reproduce the Ryu-Takayanagi formula for the entanglement entropy of a boundary region in terms of bulk properties. It has therefore been suggested that there could be an AdS/MERA correspondence, relating states in the Hilbert space of the boundary quantum system to ones defined on the bulk lattice. Here we investigate this proposal and derive necessary conditions for it to apply, using geometric features and entropy inequalities that we expect to hold in the bulk. We show that, perhaps unsurprisingly, the MERA lattice can only describe physics on length scales larger than the AdS radius. Further, using the covariant entropy bound in the bulk, we show that there are no conventional MERA parameters that completely reproduce bulk physics even on super-AdS scales. We suggest modifications or generalizations of this kind of tensor network that may be able to provide a more robust correspondence.

 

[Jimster41]

So Physics Monkey is Brian Swingle.

Gulp.

Probably a good thing I'm not aware of how big the dogs are around this place.

Very much appreciate the opportunity to listen in and ask questions.

 

[Jimster41]

Can't help it, w/respect to the lattices (got the paper printed off, and just this one little crookedly-legal question). If the finest grained one is on the bottom, how high do you think the stack of coarser and coarser grained lattices goes? Does it stop at electrons, atoms, molecules, organisms...? And If the mechanism of evolution applies down to organisms (for sure)... how far down does it go?

 

[Lord Crc]

Can't help it, w/respect to the lattices (got the paper printed off, and just this one little crookedly-legal question). If the finest grained one is on the bottom, how high do you think the stack of coarser and coarser grained lattices goes?

Turtles, all the way up.

 

[atyy]

Can't help it, w/respect to the lattices (got the paper printed off, and just this one little crookedly-legal question). If the finest grained one is on the bottom, how high do you think the stack of coarser and coarser grained lattices goes? Does it stop at electrons, atoms, molecules, organisms...? And If the mechanism of evolution applies down to organisms (for sure)... how far down does it go?

That's a good question, and I don't know the answer. My thinking is that while that is certainly the spirit of renormalization, there cannot be a completely general automatic machine that produces all the "emergent" low energy degrees of freedom like people and cats, because the low energy degrees of freedom ultimately are approximations, which means they are wrong, and there cannot be a universal way to get a wrong answer. The "right" wrong answers we like such as people and cats have something to do with what we value as human beings.

However, there has long been an idea similar to renormalization in neurobiology and machine vision. A big object is built out of smaller parts, so we should have a network, successive stacks of which recognize bigger and bigger parts. This idea is illustrated in http://static.googleusercontent.com...n/us/archive/unsupervised_icml2012_slides.pdf (slide 6), which of course looks like the coarse grained stacks in renormalization. Amusingly, this is in fact the famous google cat detector! More formally, the restricted Boltzmann machine used in machine vision and the renormalization group http://arxiv.org/abs/1410.3831.