Condensed matter physics, area laws & LQG?

[Physics Monkey]

It's not completely clear to me what these sorts of statements mean since the high energy dof don't really exist on their own. From a condensed matter perspective the high energy modes are changing all the time and the type of low energy theory you have determines the type of RG you do e.g. scaling to a point in critical theories or scaling to a surface in fermi surface systems.

I don't know how much this really differs from the standard wilsonian picture (which we all certainly use regularly). Morally speaking it seems that the rg flow ofter wanders into difficult to navigate terrain where the effective degrees of freedom change dramatically e.g. electrons at high energy and anyons at low energy.

 

[Physics Monkey]

Area laws, condensed matter, and a little bit of holography/gravity make an appearance in an essay I wrote for FQXi http://fqxi.org/community/forum/topic/1559

Check it out and give me a vote if you like it.

 

[atyy]

I see your classic paper finally got accepted by PRD!

Here's another addition to the AdS/MERA literature:

Refined Holographic Entanglement Entropy for the AdS Solitons and AdS black Holes
Masafumi Ishihara, Feng-Li Lin, Bo Ning
"We consider the refinement of the holographic entanglement entropy on a disk region for the holographic dual theories to the AdS solitons ... based on AdS/MERA conjecture, we postulate that the IR fixed-point state for the non-extremal AdS soliton is a trivial product state."

I don't immediately see a relation between the geometrical interpretations of AdS/MERA and LQG's spin networks, but let me list the one LQG paper I know that makes an explicit but bizarre connection to AdS/CFT:

Holomorphic Factorization for a Quantum Tetrahedron
Laurent Freidel, Kirill Krasnov, Etera R. Livine
"Interestingly, the integration kernel that appears in the decomposition formula turns out to be the n-point function of bulk/boundary dualities of string theory. ... For the case n=4, the symplectic manifold in question has the interpretation of the space of “shapes” of a geometric tetrahedron with fixed face areas, and our results provide a description for the quantum tetrahedron in terms of holomorphic coherent states."

 

[atyy]

http://arxiv.org/abs/1209.3304
Constructing holographic spacetimes using entanglement renormalization
Brian Swingle
(Submitted on 14 Sep 2012)
We elaborate on our earlier proposal connecting entanglement renormalization and holographic duality in which we argued that a tensor network can be reinterpreted as a kind of skeleton for an emergent holographic space. Here we address the question of the large N limit where on the holographic side the gravity theory becomes classical and a non-fluctuating smooth spacetime description emerges. We show how a number of features of holographic duality in the large N limit emerge naturally from entanglement renormalization, including a classical spacetime generated by entanglement, a sparse spectrum of operator dimensions, and phase transitions in mutual information. We also address questions related to bulk locality below the AdS radius, holographic duals of weakly coupled large N theories, Fermi surfaces in holography, and the holographic interpretation of branching MERA. Some of our considerations are inspired by the idea of quantum expanders which are generalized quantum transformations that add a definite amount of entropy to most states. Since we identify entanglement with geometry, we thus argue that classical spacetime may be built from quantum expanders (or something like them).

Goes beyond the original AdS/MERA paper by using "we" - not sure whether that's royal or not Snow monkeys are Japanese, so it's probably the latter.

 

[Physics Monkey]

I never heard of Sun Wukong before, but I like him.

 

[atyy]

Me too! http://www.youtube.com/watch?v=mOV4JUOb9j0&feature=fvwrel

 

[atyy]

@Physics Monkey, I'm still reading your latest paper slowly, but just wanted to say that it's very nicely written that even a lay person like me can understand it! It formulates more sharply all the vague questions I've been having, and begins to answer them.

 

[Physics Monkey]

@atyy, thanks a lot for your kind comment. I'm glad you found it vaguely comprehensible.

 

[atyy]

http://arxiv.org/abs/1210.6759
Holographic Entanglement Entropy of AdS Solitons and Tensor Network States
Javier Molina-Vilaplana
(Submitted on 25 Oct 2012)
The recent proposal connecting the AdS/CFT correspondence and entanglement renormalization tensor network states (MERA) is investigated by showing that the entanglement entropy and the two point functions in a type of hybrid tensor network state composed by a finite number of MERA layers and a matrix product state (MPS) acting as a cap layer, imitate the behaviour of the holographic entanglement entropy and the two point functions in the AdS soliton geometry. Within the context of AdS/CFT, AdS solitons represent theories with a mass gap, i.e gapped systems. From these observations, an explicit connection between the entanglement structure of the tensor network and those parameters which define the AdS soliton geometry is provided.

 

[atyy]

http://arxiv.org/abs/1210.7244
Entanglement entropy in de Sitter space
Juan Maldacena, Guilherme L. Pimentel
"We then study the entanglement entropy of field theories with a gravity dual. When the dual is known, we use the proposal of [10,11] to calculate the entropy. It boils down to an extremal area problem. The answer for the entanglement entropy depends drasticallyon the properties of the gravity dual. In particular, if the gravity dual has a hyperbolic Friedman-Robertson-Walker spacetime inside, then there is a non-zero contribution at order N2 for the “interesting” piece of the entanglement entropy. Otherwise, the order N2 contribution vanishes."

 

[atyy]

It does seem that the relationship between renormalization flow and holography is not well understood. Here is an interesting article about scheme dependence.

http://arxiv.org/abs/1211.1729
Holographic interpretations of the renormalization group
Vijay Balasubramanian, Monica Guica, Albion Lawrence
(Submitted on 7 Nov 2012 (v1), last revised 27 Nov 2012 (this version, v2))
In semiclassical holographic duality, the running couplings of a field theory are conventionally identified with the classical solutions of field equations in the dual gravitational theory. However, this identification is unclear when the bulk fields fluctuate. Recent work has used a Wilsonian framework to propose an alternative identification of the running couplings in terms of non-fluctuating data; in the classical limit, these new couplings do not satisfy the bulk equations of motion. We study renormalization scheme dependence in the latter formalism, and show that a scheme exists in which couplings to single trace operators realize particular solutions to the bulk equations of motion, in the semiclassical limit. This occurs for operators with dimension $\Delta \notin \frac{d}{2} + \mathbb{Z}$, for sufficiently low momenta. We then clarify the relation between the saddle point approximation to the Wilsonian effective action ($S_W$) and boundary conditions at a cutoff surface in AdS space. In particular, we interpret non-local multi-trace operators in $S_W$ as arising in Lorentzian AdS space from the temporary passage of excitations through the UV region that has been integrated out. Coarse-graining these operators makes the action effectively local.

Not directly related, but MERA fans may like to see how other people use the word "disentangle": http://techtalks.tv/talks/opening-remarks/57645/ (13:45)

 

[atyy]

marcus has listed an interesting new paper in his bibliography. It shows the LQG people are thinking about AdS/CFT and using MERA as a tool to understand it. Swingle's original paper is cited. Bianchi needs to read the new paper too, and link it up with Friedel, Krasnov, and Livine's mysterious observation I'm also glad they are thinking about induced gravity. Weinberg and Witten explicitly say it evades their no-go theorem.

http://arxiv.org/abs/1212.5183
On the Architecture of Spacetime Geometry
Eugenio Bianchi, Robert C. Myers
(Submitted on 20 Dec 2012)
We propose entanglement entropy as a probe of the architecture of spacetime in quantum gravity. We argue that the leading contribution to this entropy satisfies an area law for any sufficiently large region in a smooth spacetime, which, in fact, is given by the Bekenstein-Hawking formula. This conjecture is supported by various lines of evidence from perturbative quantum gravity, simplified models of induced gravity and loop quantum gravity, as well as the AdS/CFT correspondence.

 

[marcus]

As I recall, Physicsmonkey indicated he was Brian Swingle earlier in this thread, so there is a PF connection! Not only does Bianchi cite Brian's paper but he and coauthor thank him in the acknowledgments, for discussions.

 

[John86]

http://arxiv.org/abs/1212.5121
Modular transformation and bosonic/fermionic topological orders in Abelian fractional quantum Hall states
Xiao-Gang Wen
(Submitted on 20 Dec 2012)
The non-Abelian geometric phases of the degenerate ground states was proposed as a physically measurable defining properties of topological order in 1990. In this paper we discuss in detail such a quantitative characterization of topological order, using generic Abelian fractional quantum Hall states as examples. We show that the non-Abelian geometric phases not only contain information about the quasi-particle statistics, they also contain information about the Hall viscosity and the chiral central charge of the edge states. The chiral central charge appears as the universal 1/A correction to the Hall viscosity (where A is the area of the space). Thus, the non-Abelian geometric phases (both the Abelian part and the non-Abelian part) may provide a way to completely characterize 2D topological order. Also the non-Abelian part of the geometric phases gives rise to a projective representation of the modular group (or SL(2,Z)).

http://arxiv.org/abs/1212.4863
Boundary Degeneracy of Topological Order
Juven Wang, Xiao-Gang Wen
(Submitted on 19 Dec 2012)
We introduce the notion of boundary degeneracy of topologically ordered states on a compact orientable spatial manifold with boundaries, and emphasize that it provides richer information than the bulk degeneracy. Beyond the bulk-edge correspondence, we find the ground state degeneracy of fully gapped edge states depends on boundary gapping conditions. We develop a quantitative description of different types of boundary gapping conditions by viewing them as different ways of non-fractionalized particle condensation on the boundary. This allows us to derive the ground state degeneracy formula in terms of boundary gapping conditions, which reveals the fusion algebra of fractionalized quasiparticles. We apply our results to Toric code and Levin-Wen string-net models. By measuring the boundary degeneracy on a cylinder, we predict Z_k gauge theory and U(1)_k x U(1)_k non-chiral fractional quantum hall state at even integer k can be experimentally distinguished. Our works refine definitions of symmetry protected topological order and intrinsic topological order.

http://arxiv.org/abs/1212.2121
2D Lattice Model Construction of Symmetry-Protected Topological Phases
Peng Ye, Xiao-Gang Wen
(Submitted on 10 Dec 2012)
We propose a general approach to construct symmetry protected topological (SPT) states (ie the short-range entangled states with symmetry) in 2D spin/boson systems on lattice. In our approach, we fractionalize spins/bosons into different fermions, which occupy nontrivial Chern bands. After the Gutzwiller projection of the free fermion state obtained by filling the Chern bands, we can obtain SPT states on lattice. In particular, we constructed a U(1) SPT state, a SO(3) SPT state, and a SU(2) SPT state on lattice.

http://arxiv.org/abs/1212.1827
Quantized topological terms in weak-coupling gauge theories with symmetry and their connection to symmetry enriched topological phases
Ling-Yan Hung, Xiao-Gang Wen
(Submitted on 8 Dec 2012)
We study the quantized topological terms in a weak-coupling gauge theory with gauge group $G_g$ and a global symmetry $G_s$ in $d$ space-time dimensions. We show that the quantized topological terms are classified by a pair $(G,\nu_d)$, where $G$ is an extension of $G_s$ by $G_g$ and $\nu_d$ an element in group cohomology $\mathcal{H}^d(G,\R/\Z)$. When $d=3$ and/or when $G_s$ is finite, the weak-coupling gauge theories with quantized topological terms describe gapped symmetry enriched topological (SET) phases (ie gapped long-range entangled phases with symmetry). Thus those SET phases are classified by $\mathcal{H}^d(G,\R/\Z)$, where $G/G_g=G_s$. We also apply our theory to a simple case $G_s=G_g=Z_2$, which leads to 12 different SET phases where quasiparticles have different patterns of fractional $G_s=Z_2$ quantum numbers and fractional statistics. If the weak-coupling gauge theories are gapless, then the different quantized topological terms may describe different gapless phases of the gauge theories with a symmetry $G_s$, which may lead to different fractionalizations of $G_s$ quantum numbers and different fractional statistics (if in 2+1D).

 

[atyy]

Not directly related, but MERA fans may like to see how other people use the word "disentangle": http://techtalks.tv/talks/opening-remarks/57645/ (13:45)

I was only kidding there - but it turns out that Jason Morton works on both tensor networks and deep learning - apparently with the same mathematics!

Andrew Critch, Jason Morton. Polynomial constraints on representing entangled qubits as matrix product states

Jason Morton, Jacob Biamonte. Undecidability in Tensor Network States

Jason Morton. https://www.ipam.ucla.edu/publications/gss2012/gss2012_10605.pdf

 

[jasonmorton]

Hey, Jason here, thanks for the mention! I absolutely do think there is a connection between MERA and Deep Learning, as mentioned in the paper with Critch. I am trying to work out the details and hope to have more news this spring.

 

[atyy]

Hey, Jason here, thanks for the mention! I absolutely do think there is a connection between MERA and Deep Learning, as mentioned in the paper with Critch. I am trying to work out the details and hope to have more news this spring.

That is very cool! I see I gave the wrong link for your paper with Critch above, so let me correct that.

http://arxiv.org/abs/1210.2812
Polynomial constraints on representing entangled qubits as matrix product states
Andrew Critch, Jason Morton
"A conjectured dictionary between tensor network state models and classical probabilistic graphical models was presented in [11]. In this dictionary, matrix product states correspond to hidden Markov models, the density matrix renormalization group (DMRG) algorithm to the forward-backward algorithm, tree tensor networks to general Markov models, projected entangled pair states (PEPS) to Markov or conditional random fields, and the multi-scale entanglement renormalization ansatz (MERA) loosely to deep belief networks. In this work we formalize the first of these correspondences and use it to algebraically characterize quantum states representable by MPS and study their identifiability."

Incidentally, I came across your work via http://keck.ucsf.edu/~surya/ thesis. He's a fellow neurobiologist who had Sturmfels on his thesis committee. His website says "Although during my graduate work I played around with black holes, eleven dimensions, and little loops of string, I am now more fascinated by the world of biology which is full of incredible amounts of data but a relative paucity of theoretical frameworks within which to interpret and understand this data." But perhaps there are black holes in the brain after all To be honest, the deep architectures are genuinely inspired by biology, and although most of the learning rules seem unphysiological, experimental neurobiologists like me do find the DNN work informative. I have to admit I find DNNs more intuituitive, and I do wonder why it's ok to transfer the weights from a DBN to a DNN.

 

[atyy]

A new paper which says that the mutual information describes entanglement at finite temperature better than the entanglement entropy. Both of Physics Monkey's AdS/MERA papers are cited.

http://arxiv.org/abs/1212.4764
Holographic Mutual Information at Finite Temperature
Willy Fischler, Arnab Kundu, Sandipan Kundu
(Submitted on 19 Dec 2012)
Using the Ryu-Takayanagi conjectured formula for entanglement entropy in the context of gauge-gravity duality, we investigate properties of mutual information between two disjoint rectangular sub-systems in finite temperature relativistic conformal field theories in d-spacetime dimensions and non-relativistic scale-invariant theories in some generic examples. In all these cases mutual information undergoes a transition beyond which it is identically zero. We study this transition in details and find universal qualitative features for the above class of theories which has holographic dual descriptions. We also obtain analytical results for mutual information in specific regime of the parameter space. This demonstrates that mutual information contains the quantum entanglement part of the entanglement entropy, which is otherwise dominated by the thermal entropy at large temperatures.

Incidentally, there was an interesting result that despite correlations diverging at criticality, the mutual information in a classical stat mech Ising model peaks away from criticality. The result seems to have been confirmed. Hoefully this means that the brain isn't critical;)

http://arxiv.org/abs/1011.4421
Mutual information in classical spin models
Johannes Wilms, Matthias Troyer, Frank Verstraete
"The total many-body correlations present in finite temperature classical spin systems are studied using the concept of mutual information. As opposed to zero-temperature quantum phase transitions, the total correlations are not maximal at the phase transition, but reach a maximum in the high temperature paramagnetic phase."

http://arxiv.org/abs/1210.5707
Information theoretic aspects of the two-dimensional Ising model
Hon Wai Lau, Peter Grassberger
"All this suggests strongly that it is the slope of the mutual information, not the mutual information itself, that diverge at the critical point."

 

[atyy]

http://arxiv.org/abs/1302.5703
Holographic Local Quenches and Entanglement Density
Masahiro Nozaki, Tokiro Numasawa, Tadashi Takayanagi
(Submitted on 22 Feb 2013)
We propose a free falling particle in an AdS space as a holographic model of local quench. Local quenches are triggered by local excitations in a given quantum system. We calculate the time-evolution of holographic entanglement entropy. We confirm a logarithmic time-evolution, which is known to be typical in two dimensional local quenches. To study the structure of quantum entanglement in general quantum systems, we introduce a new quantity which we call entanglement density and apply this analysis to quantum quenches. We show that this quantity is directly related to the energy density in a small size limit. Moreover, we find a simple relationship between the amount of quantum information possessed by a massive object and its total energy based on the AdS/CFT.

"Now we would like to consider how to describe local quenches by using tensor networks. ...

Finally we would like to ask what is the holographic origin of gravitational force."

 

[atyy]

marcus highlighted this beautiful talk by Rivasseau in his bibliography.

http://pirsa.org/13020132/
Quantum Gravity as Random Geometry
Vincent Rivasseau
Abstract: Matrix models, random maps and Liouville field theory are prime tools which connect random geometry and quantum gravity in two dimensions. The tensor track is a new program to extend this connection to higher dimensions through the corresponding notions of tensor models, colored triangulations and tensor group field theories.
27/02/2013

 

[Physics Monkey]

Tensor networks get mentioned in the abstract!

http://arxiv.org/abs/1303.1080
Time Evolution of Entanglement Entropy from Black Hole Interiors
Thomas Hartman, Juan Maldacena
(Submitted on 5 Mar 2013)
We compute the time-dependent entanglement entropy of a CFT which starts in relatively simple initial states. The initial states are the thermofield double for thermal states, dual to eternal black holes, and a particular pure state, dual to a black hole formed by gravitational collapse. The entanglement entropy grows linearly in time. This linear growth is directly related to the growth of the black hole interior measured along "nice" spatial slices. These nice slices probe the spacelike direction in the interior, at a fixed special value of the interior time. In the case of a two-dimensional CFT, we match the bulk and boundary computations of the entanglement entropy. We briefly discuss the long time behavior of various correlators, computed via classical geodesics or surfaces, and point out that their exponential decay comes about for similar reasons. We also present the time evolution of the wavefunction in the tensor network description.

 

[atyy]

http://arxiv.org/abs/1303.6716
Symmetry protected entanglement renormalization
Sukhwinder Singh, Guifre Vidal
(Submitted on 27 Mar 2013)
Entanglement renormalization is a real-space renormalization group (RG) transformation for quantum many-body systems. It generates the multi-scale entanglement renormalization ansatz (MERA), a tensor network capable of efficiently describing a large class of many-body ground states, including those of systems at a quantum critical point or with topological order. The MERA has also been proposed to be a discrete realization of the holographic principle of string theory. In this paper we propose the use of symmetric tensors as a mechanism to build a symmetry protected RG flow, and discuss two important applications of this construction. First, we argue that symmetry protected entanglement renormalization produces the proper structure of RG fixed-points, namely a fixed-point for each symmetry protected phase. Second, in the context of holography, we show that by using symmetric tensors, a global symmetry at the boundary becomes a local symmetry in the bulk, thus explicitly realizing in the MERA a characteristic feature of the AdS/CFT correspondence.

http://arxiv.org/abs/1303.6772
Renormalization of an SU(2) Tensorial Group Field Theory in Three Dimensions
Sylvain Carrozza, Daniele Oriti, Vincent Rivasseau
(Submitted on 27 Mar 2013)
We address in this paper the issue of renormalizability for SU(2) Tensorial Group Field Theories (TGFT) with geometric Boulatov-type conditions in three dimensions. We prove that tensorial interactions up to degree 6 are just renormalizable without any anomaly. Our new models define the renormalizable TGFT version of the Boulatov model and provide therefore a new approach to quantum gravity in three dimensions. Among the many new technical results established in this paper are a general classification of just renormalizable models with gauge invariance condition, and in particular concerning properties of melonic graphs, the second order expansion of melonic two point subgraphs needed for wave-function renormalization.

 

[atyy]

I wonder if this is related to the line of thought in Jason Morton's work, mentioned above in #85-87.

http://arxiv.org/abs/1301.3124
Deep learning and the renormalization group
Cédric Bény
(Submitted on 14 Jan 2013 (v1), last revised 13 Mar 2013 (this version, v4))
Renormalization group (RG) methods, which model the way in which the effective behavior of a system depends on the scale at which it is observed, are key to modern condensed-matter theory and particle physics. We compare the ideas behind the RG on the one hand and deep machine learning on the other, where depth and scale play a similar role. In order to illustrate this connection, we review a recent numerical method based on the RG---the multiscale entanglement renormalization ansatz (MERA)---and show how it can be converted into a learning algorithm based on a generative hierarchical Bayesian network model. Under the assumption---common in physics---that the distribution to be learned is fully characterized by local correlations, this algorithm involves only explicit evaluation of probabilities, hence doing away with sampling.

For a comparison with standard ideas (but maybe this implementation is not so standard), how about:

http://www.cs.utexas.edu/~dana/nn.pdf
Predictive coding in the visual cortex
Rajesh P. N. Rao and Dana H. Ballard
"Lower levels operate on smaller spatial (and possibly temporal) scales, whereas higher levels estimate signal properties at larger scales because a higher-level module predicts and estimates the responses of several lower-level modules (for example, three in Fig. 1c). Thus, the effective RF size of units increases progressively until the highest level, where the RF spans the entire input image.

 

[democrito]

This is a new version of http://arxiv.org/abs/1210.6759, with a new title and new results on AdS/MERA

Holographic Geometries of one-dimensional gapped quantum systems from Tensor Network States

Javier Molina-Vilaplana

Abstract: We investigate a recent conjecture connecting the AdS/CFT correspondence and entanglement renormalization tensor network states (MERA). The proposal interprets the tensor connectivity of the MERA states associated to quantum many body systems at criticality, in terms of a dual holographic geometry which accounts for the qualitative aspects of the entanglement and the correlations in these systems. In this work, some generic features of the entanglement entropy and the two point functions in the ground state of one dimensional gapped systems are considered through a tensor network state. The tensor network is builded up as an hybrid composed by a finite number of MERA layers and a matrix product state (MPS) acting as a cap layer. Using the holographic formula for the entanglement entropy, here it is shown that an asymptotically AdS metric can be associated to the hybrid MERA-MPS state. The metric is defined by a function that manages the growth of the minimal surfaces near the capped region of the geometry. Namely, it is shown how the behaviour of the entanglement entropy and the two point correlators in the tensor network, remains consistent with a geometric computation which only depends on this function. From these observations, an explicit connection between the entanglement structure of the tensor network and the function which defines the geometry is provided.

 

[atyy]

http://arxiv.org/abs/1305.0856
The entropy of a hole in spacetime
Vijay Balasubramanian, Bartlomiej Czech, Borun D. Chowdhury, Jan de Boer
(Submitted on 3 May 2013)
We compute the gravitational entropy of 'spherical Rindler space', a time-dependent, spherically symmetric generalization of ordinary Rindler space, defined with reference to a family of observers traveling along non-parallel, accelerated trajectories. All these observers are causally disconnected from a spherical region H (a 'hole') located at the origin of Minkowski space. The entropy evaluates to S = A/4G, where A is the area of the spherical acceleration horizon, which coincides with the boundary of H. We propose that S is the entropy of entanglement between quantum gravitational degrees of freedom supporting the interior and the exterior of the sphere H.

http://arxiv.org/abs/1305.1064
On the Mutual Information between disconnected regions in AdS/CFT
Javier Molina-Vilaplana
(Submitted on 5 May 2013)
In this note, we compute the holographic mutual information between two separated circular regions in a 3+1 dimensional gauge theory dual to AdS$_5 \times S^5$ through the AdS/CFT correspondence, in the limit in which the separation $L$ between the regions is much larger than their sizes $a$. Our calculation uses some previous results concerning the holographic computation of the long distance correlator of two distant Wilson loops. We show that in these regimes, the holographic mutual information follows a power law decaying behaviour proportional to $\sqrt{\lambda}$ with $\lambda$ the t'Hooft coupling of the gauge theory. This result contradicts a conjectured sharp vanishing of the holographic mutual information between disjoint regions for the large separation regime and has been also compared with a recent result concerning a 3+1 dimensional free CFT.

 

[marcus]

This video appeared online yesterday:
http://pirsa.org/13050027/
Asymmetry protected emergent E8 symmetry
Speaker(s): Brian Swingle
Abstract: The E8 state of bosons is a 2+1d gapped phase of matter which has no topological entanglement entropy but has protected chiral edge states in the absence of any symmetry. This peculiar state is interesting in part because it sits at the boundary between short- and long-range entangled phases of matter. When the system is translation invariant and for special choices of parameters, the edge states form the chiral half of a 1+1d conformal field theory - an E8 level 1 Wess-Zumino-Witten model. However, in general the velocities of different edge channels are different and the system does not have conformal symmetry. We show that by considering the most general microscopic Hamiltonian, in particular by relaxing the constraint of translation invariance and adding disorder, conformal symmetry remerges in the low energy limit. The disordered fixed point has all velocities equal and is the E8 level 1 WZW model. Hence a highly entangled and highly symmetric system emerges, but only when the microscopic Hamiltonian is completely asymmetric.
Date: 06/05/2013 - 4:00 pm

 

[atyy]

http://arxiv.org/abs/1305.1045
A lattice non-perturbative definition of an SO(10) chiral gauge theory and its induced standard model
Xiao-Gang Wen
(Submitted on 5 May 2013)
The standard model is a chiral gauge theory where the gauge fields couple to the right-hand and the left-hand fermions differently. The standard model is defined perturbatively and describes all elementary particles (except gravitons) very well. However, for a long time, we do not know if we can have a non-perturbative definition of standard model as a Hamiltonian quantum mechanical theory. In this paper, we propose a way to give a modified standard model (with 48 two-component Weyl fermions) a non-perturbative definition by embeding the modified standard model into a SO(10) chiral gauge theory and then putting the SO(10) chiral gauge theory on a 3D spatial lattice with a continuous time. Such a non-perturbatively defined standard model is a Hamiltonian quantum theory with a finite-dimensional Hilbert space for a finite space volum. Using the defining connection between gauge anomalies and the symmetry-protected topological orders, we show that any chiral gauge theory can be non-perturbatively defined by putting it on a lattice in the same dimension, as long as the chiral gauge theory is free of all anomalies.

http://arxiv.org/abs/1305.3621
Statistical Inference and String Theory
Jonathan J. Heckman
(Submitted on 15 May 2013)
In this note we expose some surprising connections between string theory and statistical inference. We consider a large collective of agents sweeping out a family of nearby statistical models for an M-dimensional manifold of statistical fitting parameters. When the agents making nearby inferences align along a d-dimensional grid, we find that the pooled probability that the collective reaches a correct inference is the partition function of a non-linear sigma model in d dimensions. Stability under perturbations to the original inference scheme requires the agents of the collective to distribute along two dimensions. Conformal invariance of the sigma model corresponds to the condition of a stable inference scheme, directly leading to the Einstein field equations for classical gravity. By summing over all possible arrangements of the agents in the collective, we reach a string theory. We also use this perspective to quantify how much an observer can hope to learn about the internal geometry of a superstring compactification. Finally, we present some brief speculative remarks on applications to the AdS/CFT correspondence and Lorentzian signature spacetimes.

http://arxiv.org/abs/1305.3908
Quantum Renormalization Group and Holography
Sung-Sik Lee
(Submitted on 16 May 2013)
Quantum renormalization group scheme provides a microscopic understanding of holography through a general mapping between the beta functions of underlying quantum field theories and the holographic actions in the bulk. We show that the Einstein gravity emerges as a long wavelength holographic description for a matrix field theory which has no other operator with finite scaling dimension except for the energy-momentum tensor. We also point out that holographic actions for general large N matrix field theories respect the inversion symmetry along the radial direction in the bulk if the beta functions of single-trace operators are gradient flows with respect to the target space metric set by the beta functions of double-trace operators.

 

[atyy]

I came across this by reading Motl's Maldacena, Susskind: any entanglement is a wormhole of a sort.

http://arxiv.org/abs/1306.0533
Cool horizons for entangled black holes
Juan Maldacena, Leonard Susskind
(Submitted on 3 Jun 2013)
General relativity contains solutions in which two distant black holes are connected through the interior via a wormhole, or Einstein-Rosen bridge. These solutions can be interpreted as maximally entangled states of two black holes that form a complex EPR pair. We suggest that similar bridges might be present for more general entangled states. In the case of entangled black holes one can formulate versions of the AMPS(S) paradoxes and resolve them. This suggests possible resolutions of the firewall paradoxes for more general situations.

 

[Physics Monkey]

Another couple of papers that draw some connections to MERA and holography:

arXiv:1306.0515
Passing through the Firewall
Erik Verlinde, Herman Verlinde

We propose that black hole information is encoded in non-local correlations between microscopic interior and exterior degrees of freedom. We give a simple qubit representation of this proposal, and show herein that for every black hole state, the apparent firewall can be removed via a universal, state independent unitary transformation. A central element in our discussion is the distinction between virtual qubits, which are in a specified vacuum state, and real qubits, that carry the free quantum information of the black hole. We outline how our proposal may be realized in AdS/CFT.


arXiv:1305.6694
Entanglement entropy in higher derivative holography
Arpan Bhattacharyya, Apratim Kaviraj, Aninda Sinha

We consider holographic entanglement entropy in higher derivative gravity theories. Recently Lewkowycz and Maldacena arXiv:1304.4926 have provided a method to derive the equations for the entangling surface from first principles. We use this method to compute the entangling surface in four derivative gravity. Certain interesting differences compared to the two derivative case are pointed out. For Gauss-Bonnet gravity, we show that in the regime where this method is applicable, the resulting equations coincide with proposals in the literature as well as with what follows from considerations of the stress tensor on the entangling surface. Finally we demonstrate that the area functional in Gauss-Bonnet holography arises as a counterterm needed to make the Euclidean action free of power law divergences.

 

[atyy]

I learned via Motl that Kenneth Wilson has died. His marriage of the long lines of work on renormalization in high energy physics with Kadanoff's critical insight in condensed matter is surely one of the great peaks of theoretical physics. Interestingly, according to Wikipedia, Steve White was his student. White invented the DMRG which was a stepping stone to the MERA.

 

[atyy]

marcus posted this intriguing paper that the boundary state in LQG is mixed! I'm not sure this is related to the concerns of this thread, but given that one way of getting a mixed state is via entanglement and a reduced density matrix, I thought I'd post it here too.

http://arxiv.org/abs/1306.5206
The boundary is mixed
Eugenio Bianchi, Hal M. Haggard, Carlo Rovelli
(Submitted on 21 Jun 2013)
We show that Oeckl's boundary formalism incorporates quantum statistical mechanics naturally, and we formulate general-covariant quantum statistical mechanics in this language. We illustrate the formalism by showing how it accounts for the Unruh effect. We observe that the distinction between pure and mixed states weakens in the general covariant context, and surmise that local gravitational processes are indivisibly statistical with no possible quantal versus probabilistic distinction.

 

[atyy]

Maldacena's talk at Strings 2013.

Entanglement and spacetime geometry
Talk: http://www.youtube.com/embed/C1NX8baM9vw
Slides: http://strings2013.sogang.ac.kr/design/default/data/juan_maldacena.pdf

On slide 25 he writes: " If one accepts very "quantum geometries" ". (Translation: if one accepts LQG;)

Let me also note the talk by Myers on RG Flows, Entanglement and Holography. It's very related to the concerns of this thread, but rather technical, so I mention it mainly because he has one LQG paper;)

 

[Haelfix]

On slide 25 he writes: " If one accepts very "quantum geometries" ". (Translation: if one accepts LQG;)

What they have is a very special state (the thermofield state) where they can make a kinda/sorta/not really analogy between ER and EPR. They also argue that this holds for small perturbations away from the thermofield state. Only here do they have anything that resembles a classical geometry.

For highly quantum states (say a spin singlet system) there is no obvious classical geometry, and so if you believe the ER=EPR story, the corresponding right hand side must be described by some sort of quantum geometry, who's precise form is unknown.

 

[atyy]

http://arxiv.org/abs/1307.1132
The holographic dual of an EPR pair has a wormhole
Kristan Jensen, Andreas Karch
(Submitted on 3 Jul 2013)
We construct the holographic dual of two colored quasiparticles in maximally supersymmetric Yang-Mills theory entangled in a color singlet EPR pair. In the holographic dual the entanglement is encoded in a geometry of a non-traversable wormhole on the worldsheet of the flux tube connecting the pair. This gives a simple example supporting the recent claim by Maldacena and Susskind that EPR pairs and non-traversable wormholes are equivalent descriptions of the same physics.

http://arxiv.org/abs/1307.1367
Spacetime emergence via holographic RG flow from incompressible Navier-Stokes at the horizon
Stanislav Kuperstein, Ayan Mukhopadhyay
(Submitted on 4 Jul 2013)
We show that holographic RG flow can be defined precisely such that it corresponds to emergence of spacetime. We consider the case of pure Einstein's gravity with a negative cosmological constant in the dual hydrodynamic regime. The holographic RG flow is a system of first order differential equations for radial evolution of the energy-momentum tensor and the variables which parametrize it's phenomenological form on hypersurfaces in a foliation. The RG flow can be constructed without explicit knowledge of the bulk metric provided the hypersurface foliation is of a special kind. The bulk metric can be reconstructed once the RG flow equations are solved. We show that the full spacetime can be determined from the RG flow by requiring that the horizon fluid is a fixed point in a certain scaling limit leading to the non-relativistic incompressible Navier-Stokes dynamics. This restricts the near-horizon forms of all transport coefficients, which are thus determined independently of their asymptotic values and the RG flow can be solved uniquely. We are therefore able to recover the known boundary values of almost all transport coefficients at the first and second orders in the derivative expansion. We conjecture that the complete characterisation of the general holographic RG flow, including the choice of counterterms, might be determined from the hydrodynamic regime.

 

[atyy]

http://arxiv.org/abs/0908.0591
A condensed matter interpretation of SM fermions and gauge fields
I. Schmelzer
(Submitted on 5 Aug 2009)
We present the bundle Aff(3) x C x /(R^3), with a geometric Dirac equation on it, as a three-dimensional geometric interpretation of the SM fermions. Each C x /(R^3) describes an electroweak doublet. The Dirac equation has a doubler-free staggered spatial discretization on the lattice space Aff(3) x C (Z^3). This space allows a simple physical interpretation as a phase space of a lattice of cells in R^3. We find the SM SU(3)_c x SU(2)_L x U(1)_Y action on Aff(3) x C x /(R^3) to be a maximal anomaly-free special gauge action preserving E(3) symmetry and symplectic structure, which can be constructed using two simple types of gauge-like lattice fields: Wilson gauge fields and correction terms for lattice deformations. The lattice fermion fields we propose to quantize as low energy states of a canonical quantum theory with Z_2-degenerated vacuum state. We construct anticommuting fermion operators for the resulting Z_2-valued (spin) field theory. A metric theory of gravity compatible with this model is presented too.

http://arxiv.org/abs/1208.0206
Tensor Network and Black Hole
Hiroaki Matsueda, Masafumi Ishihara, Yoichiro Hashizume
(Submitted on 1 Aug 2012)
A tensor network formalism of thermofield dynamics is introduced. The formalism relates the original Hilbert space with its tilde space by a product of two copies of a tensor network. Then, their interface becomes an event horizon, and the logarithm of the tensor rank corresponds to the black hole entropy. Eventually, multiscale entanglement renormalization anzats (MERA) reproduces an AdS black hole at finite temperature. Our finding shows rich functionalities of MERA as efficient graphical representation of AdS/CFT correspondence.

http://arxiv.org/abs/1307.1522
Global symmetries in tensor network states: symmetric tensors versus minimal bond dimension
Sukhwinder Singh, Guifre Vidal
(Submitted on 5 Jul 2013)
Tensor networks offer a variational formalism to efficiently represent wave-functions of extended quantum many-body systems on a lattice. In a tensor network N, the dimension \chi of the bond indices that connect its tensors controls the number of variational parameters and associated computational costs. In the absence of any symmetry, the minimal bond dimension \chi^{min} required to represent a given many-body wave-function |\Psi> leads to the most compact, computationally efficient tensor network description of |\Psi>. In the presence of a global, on-site symmetry, one can use a tensor network N_{sym} made of symmetric tensors. Symmetric tensors allow to exactly preserve the symmetry and to target specific quantum numbers, while their sparse structure leads to a compact description and lowers computational costs. In this paper we explore the trade-off between using a tensor network N with minimal bond dimension \chi^{min} and a tensor network N_{sym} made of symmetric tensors, where the minimal bond dimension \chi^{min}_{sym} might be larger than \chi^{min}. We present two technical results. First, we show that in a tree tensor network, which is the most general tensor network without loops, the minimal bond dimension can always be achieved with symmetric tensors, so that \chi^{min}_{sym} = \chi^{min}. Second, we provide explicit examples of tensor networks with loops where replacing tensors with symmetric ones necessarily increases the bond dimension, so that \chi_{sym}^{min} > \chi^{min}. We further argue, however, that in some situations there are important conceptual reasons to prefer a tensor network representation with symmetric tensors (and possibly larger bond dimension) over one with minimal bond dimension.

http://arxiv.org/abs/1307.1604
Can a wormhole be interpreted as an EPR pair?
H. Nikolic
(Submitted on 5 Jul 2013)
Recently, Maldacena and Susskind arXiv:1306.0533 and Jensen and Karch arXiv:1307.1132 argued that a wormhole can be interpreted as an EPR pair. We point out that a convincing justification of such an interpretation would require a quantitative evidence that correlations between two ends of the wormhole are equal to those between the members of the EPR pair. As long as the existing results do not contain such evidence, the interpretation of wormhole as an EPR pair does not seem justified.