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Condensed matter physics, area laws & LQG?

  1. Mar 31, 2015 #261
    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.
     
  2. Mar 31, 2015 #262

    atyy

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    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.
     
  3. Mar 31, 2015 #263

    atyy

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    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.
     
  4. Apr 1, 2015 #264
    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.
     
    Last edited: Apr 1, 2015
  5. Apr 2, 2015 #265
    This woke me up...
    Seems pretty topical, esp after listening to Susskind's lecture (I now get more where Condensed Matter Physics comes in to 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.
     
    Last edited: Apr 2, 2015
  6. May 9, 2015 #266

    atyy

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    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.
     
    Last edited: May 9, 2015
  7. May 12, 2015 #267
    So Physics Monkey is Brian Swingle.

    Gulp. :wideeyed:

    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.
     
  8. May 12, 2015 #268
    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?

    :wideeyed:
     
  9. May 12, 2015 #269
    Turtles, all the way up.
     
  10. May 13, 2015 #270

    atyy

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    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.
     
  11. May 13, 2015 #271

    atyy

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    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
     
  12. May 13, 2015 #272
    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?"
     
  13. May 13, 2015 #273
    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.
     
    Last edited: May 13, 2015
  14. May 15, 2015 #274
    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
     
    Last edited: May 15, 2015
  15. May 16, 2015 #275

    atyy

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    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.
     
  16. May 16, 2015 #276

    atyy

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    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.
     
    Last edited: May 17, 2015
  17. May 17, 2015 #277

    marcus

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    Dearly Missed

    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
     
  18. May 18, 2015 #278

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

    CzZjL.png

    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.
     
    Last edited: May 18, 2015
  19. May 18, 2015 #279

    atyy

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    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.
     
  20. May 18, 2015 #280
    That's a helpful contrast. And QM is a case of the later?
     
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