Condensed matter physics, area laws & LQG?

[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.

 

[atyy]

Talks from the Quantum Hamiltonian Complexity Reunion workshop at the Simons Institute for the Theory of Computing at Berkeley.
http://simons.berkeley.edu/workshops/qhc2014-reunion


Spacetime, Entropy, and Quantum Information
Patrick Hayden, Stanford University


Black Holes, Firewalls and Chaos
Stephen Shenker, Stanford University


Tensor Networks and Gravity
Mike Zaletel, Microsoft Research, Station Q


MERA and Holography
Shinsei Ryu, University of Illinois, Urbana‑Champaign


Quantum Error Correction in AdS/CFT
Daniel Harlow, Princeton University

 

[Jimster41]

Lots of fun stuff, thanks. I will look at those (long and tasty lunch breaks).

What I was playing with earlier, the question I got from reading Bhobba's article and the back and forth of the thread - are we really "introducing cut offs", or critical points, or are we just recognizing they actually exist?

I'm confused why you say that lower energy degrees of freedom are all approximations that are wrong? Staring up the stack of tensors and asking "where should I put the critical points, draw the cells? (first very shallow pass through Physics Monkey's paper last night) what causal cone of coarse-graining should I climb? through which disentanglers? to get up to higher energy? seems to assume that decision is unreal, unmade in the model. Or are you just trying to clarify the piece that's missing, the "how and why did reality choose the causal cone, the sequence of disentanglers it did?"

 

[Jimster41]

On the Self Organizing Feature Map link. I get to use neural networks all day long. I don't write them. I follow them around like an eighteenth century farmer behind a plow - a plow with neural net mules, plowing dumb coal-black data, under a baking hot sun.

It's great how customers get excited about "neural networks" and "AI". Arcane in implementation, there is an intuitive accessibility to them conceptually, as simulacrum of "mind". But, in my experience there is also a layer of skepticism there and discomfort, if not outright fear (which is very interesting) Honestly, I've watched them closely enough to know, they are just dumb mules... which are a pretty spooky. People are interested in them, but when you show them what they have done, they are like, "...Nah". Then they are like, "...show me that again,... Nah".

That "Renormalization as Deep Learning" paper. Wow. "Exactly" as my boss likes to say, to suggest he knows it all.
[Edit] that's mean. Actually I love my boss. He was a bigwig at Carnegie Mellon back in the day, and Digital. And I'm a little proud of that, to be honest, and he probably knows... most all.

I really look forward to reading that one...

Thanks again for giving all these great pointers to material.

[Edit] Spooky Mules, the way that "human body detector" and "cat detector" are spooky! Really, I mean downright scary... the eyes of the machine.

 

[Jimster41]

Talks from the Quantum Hamiltonian Complexity Reunion workshop at the Simons Institute for the Theory of Computing at Berkeley.
http://simons.berkeley.edu/workshops/qhc2014-reunion


Spacetime, Entropy, and Quantum Information
Patrick Hayden, Stanford University

Just got through this one... So great. Just so interesting. I wish he hadn't had to rush at the end.
I can't stop thinking about an evolutionary dynamics, and stitching time together (History State).

mindboggling

 

[atyy]

I'm confused why you say that lower energy degrees of freedom are all approximations that are wrong?

This isn't always the case, but generally the coarse graining by averaging over fine detail, we lose information about the fine detail that is not relevant if we are just doing a coarse measurement such as a low energy measurement.

An analogy is that we to recognize a person, we don't need to know all fine details like the colour of the socks he is wearing. So usually when we talk about a person, we usually throw away such irrelevant fine details. Because we have thrown information away, we are doing an approximation that is necessarily incomplete in some way, but not a way relevant for what we are interested in.

 

[atyy]

http://arxiv.org/abs/1505.03696
Entanglement structures in qubit systems
Mukund Rangamani, Massimiliano Rota
(Submitted on 14 May 2015)
Using measures of entanglement such as negativity and tangles we provide a detailed analysis of entanglement structures in pure states of non-interacting qubits. The motivation for this exercise primarily comes from holographic considerations, where entanglement is inextricably linked with the emergence of geometry. We use the qubit systems as toy models to probe the internal structure, and introduce some useful measures involving entanglement negativity to quantify general features of entanglement. In particular, our analysis focuses on various constraints on the pattern of entanglement which are known to be satisfied by holographic sates, such as the saturation of Araki-Lieb inequality (in certain circumstances), and the monogamy of mutual information. We argue that even systems as simple as few non-interacting qubits can be useful laboratories to explore how the emergence of the bulk geometry may be related to quantum information principles.

 

[marcus]

http://arxiv.org/abs/1505.04088
Gravitational crystal inside the black hole
H. Nikolic
(Submitted on 15 May 2015)
Crystals, as quantum objects typically much larger than their lattice spacing, are a counterexample to a frequent prejudice that quantum effects should not be pronounced at macroscopic distances. We propose that the Einstein theory of gravity only describes a fluid phase and that a phase transition of crystallization can occur under extreme conditions such as those inside the black hole. Such a crystal phase with lattice spacing of the order of the Planck length offers a natural mechanism for pronounced quantum-gravity effects at distances much larger than the Planck length. A resolution of the black-hole information paradox is proposed, according to which all information is stored in a crystal-phase remnant with size and mass much above the Planck scale.
6 pages

 

[Jimster41]

This isn't always the case, but generally the coarse graining by averaging over fine detail, we lose information about the fine detail that is not relevant if we are just doing a coarse measurement such as a low energy measurement.

I have recently been trying to understand the similarities between renormalization, a middle one third erasing Cantor Set", seen in reverse,

and an evolutionary process on a growing (finite) population. My understanding of the latter ( and its similarity to the former) is that the only change required for spontaneous "fixing" of species A (and extinction of species B) is for the finite population size to grow by one... (middle third adding in the Cantor set, Nowak's "Basic Law and One Third")

No new information need be added to either species A or B. No change to the payoff matrix or fitness functions of A and B is needed. There needs to be only one more cycle of the evolutionary game, one that only one of A OR B can win. And it's not clear to me at all that "information is lost" when A wins and B goes extinct. It is not an averaging process after the critical point. It is just the current state of an irreversible history. History seen as selection through the addition of information. And the information added was nothing but one more critical game step unit (or Planck unit).

Sure we can go and "create" some species B. But this does not rewind the process, or show Species B is somehow a "compressed" constituent of Species A, it just shows the flexibility of the future of the game, and the relatively stationary rules by which it plays.

Anyway, it's bugging and confusing me. And it feels fundamentally relevant to how "QM" renormalization is perceived.

 

[atyy]

I have recently been trying to understand the similarities between renormalization, a middle one third erasing Cantor Set", seen in reverse, and an evolutionary process on a growing (finite) population. My understanding of the latter ( and its similarity to the former) is that the only change required for spontaneous "fixing" of species A (and extinction of species B) is for the finite population size to grow by one... No new information need be added to either species A or B. No change to the payoff matrix or fitness functions of A and B is needed. There needs to be only one more cycle of the evolutionary game, one that only one of A OR B can win. And it's not clear to me at all that "information is lost" when A wins and B goes extinct. It is not an averaging process after the critical point. It is just the current state of an irreversible history. History seen as selection through the addition of information. And the information added was nothing but one more, (critical) Planck unit.

Information is not always lost by renormalization, but it typically is. The simplest cases in which information can be seen not to be lost are indeed similar to the Cantor set in that they are self-similar. The most famous case in which information is lost is the central limit theorem, where one ends up with a Gaussian distribution regardless of the distributions that went into the sum.

 

[Jimster41]

Information is not always lost by renormalization, but it typically is. The simplest cases in which information can be seen not to be lost are indeed similar to the Cantor set in that they are self-similar. The most famous case in which information is lost is the central limit theorem, where one ends up with a Gaussian distribution regardless of the distributions that went into the sum.

That's a helpful contrast. And QM is a case of the later?

 

[atyy]

That's a helpful contrast. And QM is a case of the later?

It depends, and I don't know exactly which is the case in the MERA. The typical MERA does lose information. On the other hand, the MERA is best suited for describing self-similar systems, where the renormalization typically need not lose information, so I don't know whether there is a MERA that does not lose information.

Looking at Swingle's http://arxiv.org/abs/0905.1317, he writes on p5: "The goal is to reach the ultraviolet by following the renormalization group flow backwards. This is possible because we have recorded the entire renormalization “history” of the state in the network, but subtleties remain because of the possible loss of information. In practice, the truncation error may be quite small with the proper use of disentanglers. More properly, the tensor network defines a large variational class of states for which the entanglement entropy can be computed by reversing the flow [15]".

 

[Jimster41]

I've been working on reading that paper. And I definitely got hung up on why he was worried about information loss. Seems it's partly dependent on whether or not the fundamental limit on information is considered to be discrete and bounded, or continuous and infinite. Seems like that kind-of comes around full circle to the question at hand.

Thanks for the clarification.

 

[Physics Monkey]

On the question of information loss I can say one thing.

I believe that any finite bond dimension MERA (meaning all the lines in the tensor network are finite dimensional) will not be able to exactly capture a conformal field theory (CFT) ground state. This is true even if the CFT is regulated on a lattice with a finite dimensional local Hilbert space. In this sense, then, information is lost - say about high dimension operators in the CFT.

For example, consider the so-called transverse field Ising model with Hamiltonian
$$ H = -\sum_r Z_r Z_{r+1} - g \sum_r X_r $$
where g an adjustable parameter. This model has a spin 1/2 on every site of a one dimensional chain and g plays the role of the coupling. When g=1 the Hamiltonian possesses long-range correlations in its ground state and is in fact described by the so-called Ising CFT. Vidal, Evenbly, and friends have shown that many features of this CFT can be captured using a finite bond dimension MERA, but nevertheless the exact wavefunction is not reproduced.

Recently John McGreevy and I introduced a generalization of MERA (and some other tensor networks) which we dubbed "s sourcery". We conjecture that the "s source" ansatz can exactly capture the wavefunction of a lattice regulated CFT (like the above model). One replaces the quantum circuit picture in MERA with a more general local unitary transformation (thus allowing long-distance exponentially decaying tails) which maps the (ground state of the) system at size L to the system at size L/2 times some unentangled degrees of freedom. Since the transformation is unitary and the mapping is exact, no information is lost.

More generally, I would just comment that there are many notions of renormalization, it being too useful a concept to limit to just one incarnation. So in some forms perhaps information is lost while in other versions the "history" of the flow may be preserved. In the same way, there are many kinds of tensor networks and depending on the application one may want a version where information is lost or a version where information is preserved. Bottom line: I think we ought to opt for diversity in which case maybe there isn't one right answer the question of whether information is lost.

 

[Jimster41]

Physics Monkey, Swear to god, I forgot you were on here... I am really enjoying trying to understand your paper.

(thus allowing long-distance exponentially decaying tails) which maps the (ground state of the) system at size L to the system at size L/2 times some unentangled degrees of freedom. Since the transformation is unitary and the mapping is exact, no information is lost.

that...just sends me off on a cartoon comet, on which I get to pretend I understand the things you are saying...

H=-J\sum _{ <ik> }{ { \sigma }_{ i }^{ z }{ \sigma }_{ k(\lambda ) }^{ z } } -g(\lambda )J\sum _{ i }{ { \sigma }_{ i }^{ x } }
?
I just picked \lambda to represent an unknown variable.

Look forward to hearing more.

 

[marcus]

http://arxiv.org/abs/1505.04753
Entanglement equilibrium and the Einstein equation
Ted Jacobson
(Submitted on 18 May 2015)
We show that the semiclassical Einstein equation holds if and only if the entanglement entropy in small causal diamonds is stationary at constant volume, when varied from a maximally symmetric vacuum state of geometry and quantum fields. The argument hinges on a conjecture about the variation of the conformal boost energy of quantum fields in small diamonds.
7 pages

 

[atyy]

The new paper by Jacobson seems very interesting! I was hoping he'd talk about Chirco, Haggard, Riello and Rovelli http://arxiv.org/abs/1401.5262, but he only mentions Rovelli's earlier paper.

Would anyone like to guess whether Hadamard states have anything to do with quantum expanders http://arxiv.org/abs/1209.3304?

 

[atyy]

http://arxiv.org/abs/1505.05515
Integral Geometry and Holography
Bartlomiej Czech, Lampros Lamprou, Samuel McCandlish, James Sully
(Submitted on 20 May 2015)
We present a mathematical framework which underlies the connection between information theory and the bulk spacetime in the AdS3/CFT2 correspondence. A key concept is kinematic space: an auxiliary Lorentzian geometry whose metric is defined in terms of conditional mutual informations and which organizes the entanglement pattern of a CFT state. When the field theory has a holographic dual obeying the Ryu-Takayanagi proposal, kinematic space has a direct geometric meaning: it is the space of bulk geodesics studied in integral geometry. Lengths of bulk curves are computed by kinematic volumes, giving a precise entropic interpretation of the length of any bulk curve. We explain how basic geometric concepts -- points, distances and angles -- are reflected in kinematic space, allowing one to reconstruct a large class of spatial bulk geometries from boundary entanglement entropies. In this way, kinematic space translates between information theoretic and geometric descriptions of a CFT state. As an example, we discuss in detail the static slice of AdS3 whose kinematic space is two-dimensional de Sitter space.

 

[Jimster41]

That is some wild bussiness. Very interesting. And I was able to follow more of it than I expected.

It occurs to me I had the label "bulk" flipped at the outset, wrong from the holographic point of view.

But I'm a bit confused as to why the model is one where interval relationships on the rigid, geometrically simple boundary are assigned to curves, points and shapes in the bulk, rather the other way around. Where uniform/rigid geometric objects in the bulk express variation in information content (conditional probability?) that lives on the information rich '"shape" of the boundary.

In other words what if all the geodesics in the bulk are the same (geometrically simple, or at least somehow stiff or constrained) and bulk geometry emerges as encoded-interval-relations on the boundary are passed, through them, to the bulk.

Sort of a dual made of Planck-ish strings on a "Brane" contained in a "Bulk" (where I got the inverted "Bulk" labeling).

Edit] It occurs to me that this is maybe the point, but that formulating the Integration scheme might have been a lot harder from that point of view.

Anyway, mind bending stuff. And I see they ref B. Swingle! Pretty cool.

 

[atyy]

http://arxiv.org/abs/1506.01353
Hawking Radiation Energy and Entropy from a Bianchi-Smerlak Semiclassical Black Hole
Shohreh Abdolrahimi, Don N. Page
(Submitted on 2 Jun 2015)
Eugenio Bianchi and Matteo Smerlak have found a relationship between the Hawking radiation energy and von Neumann entropy in a conformal field emitted by a semiclassical two-dimensional black hole. We compare this relationship with what might be expected for unitary evolution of a quantum black hole in four and higher dimensions. If one neglects the expected increase in the radiation entropy over the decrease in the black hole Bekenstein-Hawking A/4 entropy that arises from the scattering of the radiation by the barrier near the black hole, the relation works very well, except near the peak of the radiation von Neumann entropy and near the final evaporation. These discrepancies are calculated and discussed as tiny differences between a semiclassical treatment and a quantum gravity treatment.

http://arxiv.org/abs/1506.01353
cMERA as Surface/State Correspondence in AdS/CFT
Masamichi Miyaji, Tokiro Numasawa, Noburo Shiba, Tadashi Takayanagi, Kento Watanabe
(Submitted on 3 Jun 2015)
We present how the surface/state correspondence, conjectured in arXiv:1503.03542, works in the setup of AdS3/CFT2 by generalizing the formulation of cMERA. The boundary states in conformal field theories play a crucial role in our formulation and the bulk diffeomorphism is naturally taken into account. We give an identification of bulk local operators which reproduces correct scalar field solutions on AdS3. We also calculate the information metric for a locally excited state and show that it is given by that of 2d hyperbolic manifold, which is argued to describe the time slice of AdS3.

http://arxiv.org/abs/1506.01366
The BFSS model on the lattice
Veselin G. Filev, Denjoe O'Connor
(Submitted on 3 Jun 2015)
We study the maximally supersymmetric BFFS model at finite temperature and its bosonic relative. For the bosonic model in p+1 dimensions, we find that it effectively reduces to a system of gauged Gaussian matrix models. The effective model captures the low temperature regime of the model including the phase transition. The mass becomes p1/3λ1/3 for large p, with λ the 'tHooft coupling. For p=9 simulations of the model give m=(1.90±.01)λ1/3, which is also the mass gap of the Hamiltonian. We argue that there is no `sign' problem in the maximally supersymmetric BFSS model and perform detailed simulations of several observables finding excellent agreement with AdS/CFT predictions when 1/α′ corrections are included.

http://arxiv.org/abs/1506.01337
Violations of the Born rule in cool state-dependent horizons
Donald Marolf, Joseph Polchinski
(Submitted on 3 Jun 2015)
The black hole information problem has motivated many proposals for new physics. One idea, known as state-dependence, is that quantum mechanics must be generalized to describe the physics of black holes, and that fixed linear operators do not provide the fundamental description of experiences for infalling observers. Instead, such experiences are to be described by operators with an extra dependence on the global quantum state. We show that any implementation of this idea strong enough to remove firewalls from generic states requires massive violations of the Born rule. We also demonstrate a sense in which such violations are visible to infalling observers involved in preparing the initial state of the black hole. We emphasize the generality of our results; no details of any specific proposal for state-dependence are required.

 

[atyy]

http://arxiv.org/abs/1506.01623
Area Law from Loop Quantum Gravity
Alioscia Hamma, Ling-Yan Hung, Antonino Marciano, Mingyi Zhang
(Submitted on 4 Jun 2015)
We explore the constraints following from requiring the Area Law in the entanglement entropy in the context of loop quantum gravity. We find a unique solution to the single link wave-function in the large j limit, believed to be appropriate in the semi-classical limit. We then generalize our considerations to multi-link coherent states, and find that the area law is preserved very generically using our single link wave-function as a building block. Finally, we develop the framework that generates families of multi-link states that preserve the area law while avoiding macroscopic entanglement, the space-time analogue of "Schroedinger cat". We note that these states, defined on a given set of graphs, are the ground states of some local Hamiltonian that can be constructed explicitly. This can potentially shed light on the construction of the appropriate Hamiltonian constraints in the LQG framework.

 

[atyy]

http://arxiv.org/abs/1506.05792
Geometric entropy and edge modes of the electromagnetic field
William Donnelly, Aron C. Wall
(Submitted on 18 Jun 2015)
We calculate the vacuum entanglement entropy of Maxwell theory in a class of curved spacetimes by Kaluza-Klein reduction of the theory onto a two-dimensional base manifold. Using two-dimensional duality, we express the geometric entropy of the electromagnetic field as the entropy of a tower of scalar fields, constant electric and magnetic fluxes, and a contact term, whose leading order divergence was discovered by Kabat. The complete contact term takes the form of one negative scalar degree of freedom confined to the entangling surface. We show that the geometric entropy agrees with a statistical definition of entanglement entropy that includes edge modes: classical solutions determined by their boundary values on the entangling surface. This resolves a longstanding puzzle about the statistical interpretation of the contact term in the entanglement entropy. We discuss the implications of this negative term for black hole thermodynamics and the renormalization of Newton's constant.

 

[Berlin]

Wrong post. Sorry.

 

[atyy]

http://arxiv.org/abs/1409.6017
The Cheshire Cap
Emil J. Martinec
(Submitted on 21 Sep 2014 (v1), last revised 3 Oct 2014 (this version, v2))
A key role in black hole dynamics is played by the inner horizon; most of the entropy of a slightly nonextremal charged or rotating black hole is carried there, and the covariant entropy bound suggests that the rest lies in the region between the inner and outer horizon. An attempt to match this onto results of the microstate geometries program suggests that a `Higgs branch' of underlying long string states of the configuration space realizes the degrees of freedom on the inner horizon, while the `Coulomb branch' describes the inter-horizon region and beyond. Support for this proposal comes from an analysis of the way singularities develop in microstate geometries, and their close analogy to corresponding structures in fivebrane dynamics. These singularities signal the opening up of the long string degrees of freedom of the theory, which are partly visible from the geometry side. A conjectural picture of the black hole interior is proposed, wherein the long string degrees of freedom resolve the geometrical singularity on the inner horizon, yet are sufficiently nonlocal to communicate information to the outer horizon and beyond.

http://arxiv.org/abs/1505.05239
Fractionated Branes and Black Hole Interiors
Emil J. Martinec
(Submitted on 20 May 2015)
Combining a variety of results in string theory and general relativity, a picture of the black hole interior is developed wherein spacetime caps off at an inner horizon, and the inter-horizon region is occupied by a Hagedorn gas of a very low tension state of fractionated branes. This picture leads to natural resolutions of a variety of puzzles concerning quantum black holes. Gravity Research Foundation 2015 Fourth Prize Award for Essays on Gravitation.

http://arxiv.org/abs/1506.04342
A model with no firewall
Samir D. Mathur
(Submitted on 14 Jun 2015)
We construct a model which illustrates the conjecture of fuzzball complementarity. In the fuzzball paradigm, the black hole microstates have no interior, and radiate unitarily from their surface through quanta of energy E∼T. But quanta with E≫T impinging on the fuzzball create large collective excitations of the fuzzball surface. The dynamics of such excitations must be studied as an evolution in superspace, the space of all fuzzball solution |Fi⟩. The states in this superspace are arranged in a hierarchy of `complexity'. We argue that evolution towards higher complexity maps, through a duality analogous to AdS/CFT, to infall inside the horizon of the traditional hole. We explain how the large degeneracy of fuzzball states leads to a breakdown of the principle of equivalence at the threshold of horizon formation. We recall that the firewall argument did not invoke the limit E≫T when considering a complementary picture; on the contrary it focused on the dynamics of the E∼T modes which contribute to Hawking radiation. This loophole allows the dual description conjectured in fuzzball complementarity.

 

[atyy]

http://arxiv.org/abs/1403.2048
Era of Big Data Processing: A New Approach via Tensor Networks and Tensor Decompositions
Andrzej Cichocki

http://www.unige.ch/math/vandereycken/bibtexbrowser.php?key=Uschmajew_V_2013&bib=my_pubs.bib
The geometry of algorithms using hierarchical tensors
A. Uschmajew, B. Vandereycken
In this paper, the differential geometry of the novel hierarchical Tucker format for tensors is derived. The set HT_k of tensors with fixed tree T and hierarchical rank k is shown to be a smooth quotient manifold, namely the set of orbits of a Lie group action corresponding to the non-unique basis representation of these hierarchical tensors. Explicit characterizations of the quotient manifold, its tangent space and the tangent space of HT_k are derived, suitable for high-dimensional problems. The usefulness of a complete geometric description is demonstrated by two typical applications. First, new convergence results for the nonlinear Gauss--Seidel method on HT_k are given. Notably and in contrast to earlier works on this subject, the task of minimizing the Rayleigh quotient is also addressed. Second, evolution equations for dynamic tensor approximation are formulated in terms of an explicit projection operator onto the tangent space of HT_k. In addition, a numerical comparison is made between this dynamical approach and the standard one based on truncated singular value decompositions.

 

[atyy]

Pointed out by julian in https://www.physicsforums.com/threads/lqg-and-gravity.821182/#post-5156055

https://workspace.imperial.ac.uk/th...ic%2FMSc%2FDissertations%2F2014&CurrentPage=1
Entanglement on Spin Networks in Loop Quantum Gravity
Clement Delcamp

 

[atyy]

http://arxiv.org/abs/1507.00354
Covariant Constraints on Hole-ography
Netta Engelhardt, Sebastian Fischetti
(Submitted on 1 Jul 2015)
Hole-ography is a prescription relating the areas of surfaces in an AdS bulk to the differential entropy of a family of intervals in the dual CFT. In (2+1) bulk dimensions, or in higher dimensions when the bulk features a sufficient degree of symmetry, we prove that there are surfaces in the bulk that cannot be completely reconstructed using known hole-ographic approaches, even if extremal surfaces reach them. Such surfaces lie in easily identifiable regions: the interiors of holographic screens. These screens admit a holographic interpretation in terms of the Bousso bound. We speculate that this incompleteness of the reconstruction is a form of coarse-graining, with the missing information associated to the holographic screen. We comment on perturbative quantum extensions of our classical results.

http://arxiv.org/abs/1507.00591
AdS/CFT without holography: A hidden dimension on the CFT side and implications for black-hole entropy
H. Nikolic
(Submitted on 2 Jul 2015)
We propose a new non-holographic formulation of AdS/CFT correspondence, according to which quantum gravity on AdS and its dual non-gravitational field theory both live in the same number D of dimensions. The field theory, however, appears (D-1)-dimensional because the interactions do not propagate in one of the dimensions. The D-dimensional action for the field theory can be identified with the sum over (D-1)-dimensional actions with all possible values Λ of the UV cutoff, so that the extra hidden dimension can be identified with Λ. Since there are no interactions in the extra dimension, most of the practical results of standard holographic AdS/CFT correspondence transcribe to non-holographic AdS/CFT without any changes. However, the implications on black-hole entropy change significantly. The maximal black-hole entropy now scales with volume, while the Bekenstein-Hawking entropy is interpreted as the minimal possible black-hole entropy. In this way, the non-holographic AdS/CFT correspondence offers a simple resolution of the black-hole information paradox, consistent with a recently proposed gravitational crystal.

 

[atyy]

http://arxiv.org/abs/1507.03836
Perturbative entanglement thermodynamics for AdS spacetime: Renormalization
Rohit Mishra, Harvendra Singh
(Submitted on 14 Jul 2015)
We study the effect of charged excitations in the AdS spacetime on the first law of entanglement thermodynamics. It is found that `boosted' AdS black holes give rise to a more general form of first law which includes chemical potential and charge density. To obtain this result we have to resort to a second order perturbative calculation of entanglement entropy for small size subsystems. At first order the form of entanglement law remains unchanged even in the presence of charged excitations. But the thermodynamic quantities have to be appropriately `renormalized' at the second order due to the corrections. We work in the perturbative regime where Tthermal≪TE.

http://arxiv.org/abs/1507.04130
Bulk Locality and Boundary Creating Operators
Yu Nakayama, Hirosi Ooguri
(Submitted on 15 Jul 2015)
We formulate a minimum requirement for CFT operators to be localized in the dual AdS. In any spacetime dimensions, we show that a general solution to the requirement is a linear superposition of operators creating spherical boundaries in CFT, with the dilatation by the imaginary unit from their centers. This generalizes the recent proposal by Miyaji et al. for bulk local operators in the three dimensional AdS. We show that Ishibashi states for the global conformal symmetry in any dimensions and with the imaginary dilatation obey free field equations in AdS and that incorporating bulk interactions require their superpositions. We also comment on the recent proposals by Kabat et al., and by H. Verlinde.

http://arxiv.org/abs/1507.04633
Entanglement renormalization and integral geometry
Xing Huang, Feng-Li Lin
(Submitted on 16 Jul 2015)
We revisit the applications of integral geometry in AdS3 and argue that the volume form of the kinematic space can be understood as a measure of entanglement between the end points of a geodesic. We explain how this idea naturally fits into the picture of entanglement renormalization of an entangled pair, from which we can holographically understand the operations of disentangler and isometry in multi-scale entanglement renormalization ansatz (MERA). A renormalization group (RG) equation of the long-distance entanglement is then derived, which indicates how the entanglement is reshuffled by holographic isometry operation. We then generalize this integral geometric construction to higher dimensional bulk space of homogeneity and isotropy.

 

[atyy]

http://arxiv.org/abs/1507.06410
Generalized entanglement entropy
Marika Taylor
(Submitted on 23 Jul 2015)
We discuss two measures of entanglement in quantum field theory and their holographic realizations. For field theories admitting a global symmetry, we introduce a global symmetry entanglement entropy, associated with the partitioning of the symmetry group. This quantity is proposed to be related to the generalized holographic entanglement entropy defined via the partitioning of the internal space of the bulk geometry. The second measure of quantum field theory entanglement is the field space entanglement entropy, obtained by integrating out a subset of the quantum fields. We argue that field space entanglement entropy cannot be precisely realized geometrically in a holographic dual. However, for holographic geometries with interior decoupling regions, the differential entropy provides a close analogue to the field space entanglement entropy. We derive generic descriptions of such inner throat regions in terms of gravity coupled to massive scalars and show how the differential entropy in the throat captures features of the field space entanglement entropy.

 

[atyy]

http://arxiv.org/abs/1507.07555
Gravity Dual of Quantum Information Metric
Masamichi MIyaji, Tokiro Numasawa, Noburo Shiba, Tadashi Takayanagi, Kento Watanabe
(Submitted on 27 Jul 2015)
We study a quantum information metric (or fidelity susceptibility) in conformal field theories with respect to a small perturbation by a primary operator. We argue that its gravity dual is approximately given by a volume of maximal time slice in an AdS spacetime when the perturbation is exactly marginal. We confirm our claim in several examples.

 

[atyy]

http://arxiv.org/abs/1508.00897
Canonical Energy is Quantum Fisher Information
Nima Lashkari, Mark Van Raamsdonk
(Submitted on 4 Aug 2015)
In quantum information theory, Fisher Information is a natural metric on the space of perturbations to a density matrix, defined by calculating the relative entropy with the unperturbed state at quadratic order in perturbations. In gravitational physics, Canonical Energy defines a natural metric on the space of perturbations to spacetimes with a Killing horizon. In this paper, we show that the Fisher information metric for perturbations to the vacuum density matrix of a ball-shaped region B in a holographic CFT is dual to the canonical energy metric for perturbations to a corresponding Rindler wedge R_B of Anti-de-Sitter space. Positivity of relative entropy at second order implies that the Fisher information metric is positive definite. Thus, for physical perturbations to anti-de-Sitter spacetime, the canonical energy associated to any Rindler wedge must be positive. This second-order constraint on the metric extends the first order result from relative entropy positivity that physical perturbations must satisfy the linearized Einstein's equations.