Condensed matter physics, area laws & LQG?

atyy

Newly posted by marcus at his bibliography. These guys are on the case! They cite and make use of the paper that started this thread.

http://arxiv.org/abs/1109.4927
Coarse graining methods for spin net and spin foam models
Bianca Dittrich, Frank C. Eckert, Mercedes Martin-Benito
(Submitted on 22 Sep 2011)
We undertake first steps in making a class of discrete models of quantum gravity, spin foams, accessible to a large scale analysis by numerical and computational methods. In particular, we apply Migdal-Kadanoff and Tensor Network Renormalization schemes to spin net and spin foam models based on finite Abelian groups and introduce `cutoff models' to probe the fate of gauge symmetries under various such approximated renormalization group flows. For the Tensor Network Renormalization analysis, a new Gauss constraint preserving algorithm is introduced to improve numerical stability and aid physical interpretation. We also describe the fixed point structure and establish an equivalence of certain models.

czes

I am desperately looking for a solution of the quantization paradox in the Quantum Gravity with regard to the observation of the GRB from the distant galaxy. Is the universe at the deepest level grainy?
We exclude the random walk model and most of the holographic models of the space-time foam.
http://www.centauri-dreams.org/?p=18718

May be , we have to distinguish the different kinds of the discretness ?

atyy

I hope they post lectures online! Bolding below is mine.

http://www.perimeterinstitute.ca/Eve...ield_Theories/
Tensor Networks for Quantum Field Theories
October 24 - 25, 2011
Perimeter Institute

Tensor network states, such as the matrix product state (MPS), projected entangled-pair states (PEPS), and the multi-scale entanglement renormalization ansatz (MERA), can be used to efficiently represent the ground state of quantum many-body Hamiltonians on a lattice. In this way, they provide a novel theoretical framework to characterize phases of quantum matter, while also being the basis for powerful numerical approaches to strongly interacting systems on the lattice.

The goal of this meeting is to discuss recent extensions of tensor network techniques to continuous systems. Continuous MPS and continuous MERA can tackle quantum field theories directly, without the need to put them on the lattice. Therefore they offer a non-perturbative, variational approach to QFT, with plenty of potential applications. On the other hand, the proposal of continuous MERA makes previous hand-waving arguments that the MERA is a lattice realization of the AdS/CFT correspondence ever more intriguing.

Pedagogical talks will be directed to introducing the subject to (PI resident) quantum field/string theorists. Discussions with the latter will aim at identifying future applications and challenges.

Scientific Organizers:
Guifre Vidal, Perimeter Institute
Frank Verstraete, University of Vienna

atyy

http://arxiv.org/abs/1109.5592
Connecting Entanglement Renormalization and Gauge/Gravity dualities
Javier Molina-Vilaplana
(Submitted on 26 Sep 2011)
I propose a connection between the Multi-Scale Entanglement Renormalization Ansatz (MERA) and holographic gravity duals. The relationship is provided by analyzing the renormalization group (RG) flow of correlation functions in MERA and showing their formal equivalence with the holographic RG flow of these correlation functions in Anti de Sitter (AdS) space. As a corollary, we argue that when considering correlations between disjoint regions, the holographic dual of the MERA procedure may be efficiently described by an AdS black hole.

qsa

Nature is fundamentally a statistical system i.e. discrete at heart (must be), but let me give you a simple analogy. throwing a coin ,you might get 3045 heads and 89080 tails, that is discrete to be sure . But the ratio is real. so Nature is fundamentally discrete but you never measure that discreteness (you can't) , we can only measure the ratio like numbers to certain accuracy. So there it is, no conflict.

atyy

marcus posted in his bibliography a really interesting in GFT renormalization. The Dittrich et al paper in post #35 is aware of the tensor-network stuff in which the lattice is fixed, and this stuff, in which the several lattices are summed over. The Feynman diagrams of GFT are spin foams.

http://arxiv.org/abs/1111.4997
A Renormalizable 4-Dimensional Tensor Field Theory
Joseph Ben Geloun, Vincent Rivasseau
(Submitted on 21 Nov 2011)
We prove that an integrated version of the Gurau colored tensor model supplemented with the usual Bosonic propagator on U(1)4 is renormalizable to all orders in perturbation theory. The model is of the type expected for quantization of space-time in 4D Euclidean gravity and is the first example of a renormalizable model of this kind. Its vertex and propagator are four-stranded like in 4D group field theories, but without gauge averaging on the strands. Surprisingly perhaps, the model is of the φ6 rather than of the φ4 type, since two different φ6-type interactions are log-divergent, i.e. marginal in the renormalization group sense. The renormalization proof relies on a multiscale analysis. It identifies all divergent graphs through a power counting theorem. These divergent graphs have internal and external structure of a particular kind called melonic. Melonic graphs dominate the 1/N expansion of colored tensor models and generalize the planar ribbon graphs of matrix models. A new locality principle is established for this category of graphs which allows to renormalize their divergences through counterterms of the form of the bare Lagrangian interactions. The model also has an unexpected anomalous log-divergent (∫φ2)2 term, which can be interpreted as the generation of a scalar matter field out of pure gravity.
41 pages, 9 figures

atyy

MTd2 alerts us on marcus's bibliography to Rivasseau's latest manifesto. If we count TFT as LQG inspired, then it contains another explicit declaration of a search for AdS/LQG: "TFT should certainly benefit from this beautiful circle of ideas, for instance from the possibility of identifying the radial direction in AdS-CFT with the RG scale. There are some preliminary glimpses of a possible holographic nature of the boundary of colored tensor graphs."

Key points of the TFT manifesto:

"TFT can in particular include the study of renormalizable GFT models, which are similar to combinatorial models but with an additional gauge invariance."

"There is a strong link between the universal character of the central limit theorem in probability theory and the existence of a 1/N expansion"

"We saw already that there is a parallel between the hierarchy of central limit theorems in probability theory and the hierarchy of 1/N expansions in quantum field theory. There is also an associated hierarchy of renormalization group types: scalar, vector, matrix, tensors. They can be distinguished by their different notions of locality and the different power counting formulas to which they lead to."

"We know the renormalization group type can change along a given RG trajectory at a phase transition point. For instance at the BCS transition in condensed matter, the RG type changes form vector to scalar. There is therefore no reason the RG cannot change from tensor to lower-rank type at geometrogenesis."

Physics Monkey

Not sure what this means.

atyy

I sent Vincent Rivasseau an email asking for some pointers to the literature that describes the RG type change in BCS theory. He sent me the following to post. He didn't post directly, because he was a bit afraid of spending too much time here, but indicated he might register if there's growing discussion. Vincent - thanks so much!

----------------------------------
Reply from Vincent Rivasseau
----------------------------------

The renormalization group in condensed matter was investigated in the 90's through modern field theoretic techniques by a group of mathematical physicists, including in particular Benfatto, Feldman, Gallavotti, Magnen, Trubowitz and myself.

We understood that in two space dimensions or more, the extended character of the Fermi surface singularity leads to a
RG very different from the (scalar) RG of ordinary QFT, which is governed by the point singularity of 1/p^2 at p=0. In particular the power counting is independent of the space-time dimension, and the leading graphs are chains of bubbles, similar to the ones leading the 1/N expansion of vector models.
This is because the leading elementary 4point graph is a certain type of bubble at zero external momentum.
Indeed at external momentum P the momenta q and q+P on the two lines of the bubble cannot run both over the full Fermi singularity; only at P=0 (for parity invariant Fermi singularities) there is maximal coincidence between the extended singularity on the two lines. There is also a related notion of locality, which works only for the leading graphs: indeed only for these graphs (at P=0) there is a phase cancellation which allows renormalization by a local counterterm of the initial Lagrangian type. Hence it is really a new RG type (in the sense used in the tensor track paper).

This was first explained in
An Intrinsic 1/N Expansion for Many Fermion System, avec J. Feldman, J. Magnen et E. Trubowitz, Europhys. Letters 24, 437 (1993). 35.
R. Shankar also wrote a pedagogic review on this, namely
Renormalization-group approach to interacting Fermions,
Rev Mod Phys 66 129-192 (1994).

There is in the BCS theory a phase transition namely the formation of the Cooper pair which is a Boson. Its propagator is the sum of the chain of bubbles of the Fermionic theory. But it has no Fermi surface. Hence the power counting for that resulting Boson behaves in the infrared as an ordinary 1/p^2 propagator, and this effect can be studied in detail. Therefore BCS is a well-understood case of change of RG type from vector to scalar type (see eg arXiv.cond-mat/9503047).

The hope is that the leading graphs of a suitable renormalizable TFT could generate the propagator of the graviton. If this is turns out to be true, the main problem of non-renormalizability of QG on ordinary space time would be solved in a satisfying way, ie without imposing an arbitrary cutoff on the theory. A more complicated and perhaps more realistic scenario would involve a cascade of transitions, eg from tensor to matrix (ie non commutative QFT's), then from matrix to vectors and scalars. Such a more complicated scenario could perhaps accomodate better the matter fields of the standard model and their interactions.

Best wishes
V. Rivasseau

atyy

I'm not sure Giddings's new paper is related to the tensor networks of condensed matter physics, but he does say "tensor network"! He also says that if AdS/CFT works, then maybe he is describing something that is part of AdS/CFT, which sounds a bit like this. With quantum mechanics maybe giving rise to statistical mechanics, Zurek's proposed derivation of the Born rule, and all the Bell's theorem stuff, I think it makes sense to imagine that evolution is still unitary for this round of the game.

http://arxiv.org/abs/1201.1037
Black holes, quantum information, and unitary evolution
Steven B. Giddings

atyy

Giddings has a talk about his stuff. In discussions with the audience it is mentioned that this seems similar to stuff from quantum information theory. Evenbly's thesis reviews the quantum circuit interpretation of MERA, as well as Swingle's idea that MERA and AdS/CFT are related.

Hilbert Space Networks and Unitary Models for Black Hole Evolution
http://online.itp.ucsb.edu/online/bitbranes12/giddings/

atyy

Hardy has remarks on quantum gravity in the final section of his essay. Markopoulou's quantum causal histories and Vidal's MERA are cited.

http://arxiv.org/abs/1201.4390
The Operator Tensor Formulation of Quantum Theory
Lucien Hardy

"The challenge of setting up quantum field theory is to work out how to take the limit of this situation to the infinitesimal (rather than discrete) case. However, this framework offers certain advantages as an approach to quantum field theory. Namely, it provides a formulation which is in keeping with the spirit of special relativity without necessary reference to any specific foliation.

This framework might also provide a good stepping stone to a theory of quantum gravity. Formalism locality, as a desirable property, was motivated by considerations from quantum gravity [29]."

One great challenge facing applying these techniques to quantum field theory and, possibly, to quantum gravity, is to know how to adapt or reproduce that relevant physics which is usually formulated in terms of differential equations using the Turing inspired ideas of computer science.

atyy

Jacobson gave an interesting talk Vacuum Entanglement Entropy, Horizon Thermodynamics and Gravitation. He mentions that entanglement is related to the rigidity of spacetime.

Before that van Raamsdonk had an equally interesting talk about Rindler quantum gravity. The paper by Czech et al The Gravity Dual of a Density Matrix says "Conversely, knowledge of the bulk geometry at successively greater distance from the boundary requires knowledge of entanglement at successively longer scales" with an explicit citation of Swingle's observations about MERA and holography.

marcus

That talk by Jacobson is great.
http://online.kitp.ucsb.edu/online/b..._c12/jacobson/
In line with what you said, he relates the amount of entanglement across an horizon with 1/G the reciprocal of the Newton constant. G measures how easily the geometry can be deformed by stress-energy and so the reciprocal 1/G is a measure of "stiffness"

The talk itself is some 31 minutes, if I remember, but then with questions it runs to 44 minutes.
The essential, highly accessible portion I would say, is the first 18 or 19 minutes which REVIEWS the famous ideas of GR as the equation of state of unspecfied micro degrees of freedom. I would strongly recommend the first 18 or so minutes.

After that he talks about higher curvature terms and generalizations---newer work.

Rafael Sorkin is there and asks questions. Also Erik or Hermann Verlinde. Gary Gibbons also converses with TJ at the end.

marcus

That talk by Jacobson is great.
http://online.kitp.ucsb.edu/online/b..._c12/jacobson/
In line with what you said, he relates the amount of entanglement across an horizon with 1/G the reciprocal of the Newton constant. G measures how easily the geometry can be deformed by stress-energy and so the reciprocal 1/G is a measure of "stiffness"

The talk is some 31 minutes, if I remember, but then with questions it runs to 44 minutes.
The essential, highly accessible portion I would say, is the first 18 or 19 minutes which REVIEWS the famous ideas of GR as the equation of state of unspecfied micro degrees of freedom. I would strongly recommend the first 18 or so minutes.

After that he talks about higher curvature terms and generalizations---newer work.

Sorkin is there and asks questions.

atyy

Basic question about the Jacobson stuff: in the Clausius relation dS=dQ/T, I think the heat flow must be reversible. Why is the energy flow across the horizon reversible?

atyy

Donnelly has a paper about the entanglement entropy of lattice gauge theory in the language of LQG - spin networks, intertwiners etc. It's interesting because of work on the holographic entanglement entropy, which is reviewed by Takayanagi.

http://arxiv.org/abs/1109.0036
Decomposition of entanglement entropy in lattice gauge theory
William Donnelly

"We note also that the Hilbert space of edge states in SU(2) lattice gauge theory is closely related to the Hilbert space of the SU(2) Chern-Simons theory whose states are counted in the loop quantum gravity derivation of black hole entropy [22, 23]."

http://arxiv.org/abs/1204.2450
Entanglement Entropy from a Holographic Viewpoint
Tadashi Takayanagi

"The upshot is that the area of a minimal surface in a (Euclidean) gravitational theory corresponds to the entanglement entropy in its dual non-gravitational theory"

"The lattice calculations [86, 87] (see also [88]) of pure Yang-Mills theory qualitatively confirm this prediction from AdS/CFT, though the order of phase transition is no longer first order for these finite N calculations."