
#1
Feb810, 01:20 AM

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I think Markopoulou and Oriti have been sniffing this out a long time. Note that Wen has heuristically linked tensor networks and AdS/CFT (strings!) in the final slide of http://dao.mit.edu/~wen/talks/09QHtop.pdf.
http://arxiv.org/abs/0907.2994 Tensor network decompositions in the presence of a global symmetry Sukhwinder Singh, Robert N. C. Pfeifer, Guifre Vidal (Submitted on 17 Jul 2009) Tensor network decompositions offer an efficient description of certain manybody states of a lattice system and are the basis of a wealth of numerical simulation algorithms. We discuss how to incorporate a global symmetry, given by a compact, completely reducible group G, in tensor network decompositions and algorithms. This is achieved by considering tensors that are invariant under the action of the group G. Each symmetric tensor decomposes into two types of tensors: degeneracy tensors, containing all the degrees of freedom, and structural tensors, which only depend on the symmetry group. In numerical calculations, the use of symmetric tensors ensures the preservation of the symmetry, allows selection of a specific symmetry sector, and significantly reduces computational costs. On the other hand, the resulting tensor network can be interpreted as a superposition of exponentially many spin networks. Spin networks are used extensively in loop quantum gravity, where they represent states of quantum geometry. Our work highlights their importance also in the context of tensor network algorithms, thus setting the stage for crossfertilization between these two areas of research. http://arxiv.org/abs/0808.3773 Area laws for the entanglement entropy  a review Authors: J. Eisert, M. Cramer, M.B. Plenio (Submitted on 28 Aug 2008 (v1), last revised 16 Jan 2009 (this version, v3)) Physical interactions in quantum manybody systems are typically local: Individual constituents interact mainly with their few nearest neighbors. This locality of interactions is inherited by a decay of correlation functions, but also reflected by scaling laws of a quite profound quantity: The entanglement entropy of ground states. This entropy of the reduced state of a subregion often merely grows like the boundary area of the subregion, and not like its volume, in sharp contrast with an expected extensive behavior. Such "area laws" for the entanglement entropy and related quantities have received considerable attention in recent years. They emerge in several seemingly unrelated fields, in the context of black hole physics, quantum information science, and quantum manybody physics where they have important implications on the numerical simulation of lattice models. In this Colloquium we review the current status of area laws in these fields. Center stage is taken by rigorous results on lattice models in one and higher spatial dimensions. The differences and similarities between bosonic and fermionic models are stressed, area laws are related to the velocity of information propagation, and disordered systems, nonequilibrium situations, classical correlation concepts, and topological entanglement entropies are discussed. A significant proportion of the article is devoted to the quantitative connection between the entanglement content of states and the possibility of their efficient numerical simulation. We discuss matrixproduct states, higherdimensional analogues, and states from entanglement renormalization and conclude by highlighting the implications of area laws on quantifying the effective degrees of freedom that need to be considered in simulations. http://arxiv.org/abs/0809.2393 Explicit tensor network representation for the ground states of stringnet models O. Buerschaper, M. Aguado, G. Vidal (Submitted on 14 Sep 2008) The structure of stringnet lattice models, relevant as examples of topological phases, leads to a remarkably simple way of expressing their ground states as a tensor network constructed from the basic data of the underlying tensor categories. The construction highlights the importance of the fat lattice to understand these models. 



#2
Feb910, 12:08 AM

P: 716

Condensation and evolution of spacetime network
Authors: Bi Qiao (Submitted on 29 Sep 2008) Abstract: In this work, we try to propose, in a novel way using the Bose and Fermi quantum network approach, a framework studying condensation and evolution of space time network described by the Loop quantum gravity. Considering quantum network connectivity features in the Loop quantum gravity, we introduce a link operator, and through extending the dynamical equation for the evolution of quantum network posed by Ginestra Bianconi to an operator equation, we get the solution of the link operator. This solution is relevant to the Hamiltonian of the network, and then is related to the energy distribution of network nodes. Showing that tremendous energy distribution induce huge curved spacetime network, may have space time condensation in highenergy nodes. For example, in the black hole circumstances, quantum energy distribution is related to the area, thus the eigenvalues of the link operator of the nodes can be related to quantum number of area, and the eigenvectors are just the spin network states. This reveals that the degree distribution of nodes for spacetime network is quantized, which can form the spacetime network condensation. The black hole is a sort of result of spacetime network condensation, however there may be more extensive spacetime network condensation, for example, the universe singularity (big bang). Quantum gravity as a Fermi liquid Authors: Stephon H.S. Alexander, Gianluca Calcagni (Submitted on 1 Jul 2008 (v1), last revised 21 Nov 2008 (this version, v2)) Abstract: We present a reformulation of loop quantum gravity with a cosmological constant and no matter as a Fermiliquid theory. When the topological sector is deformed and large gauge symmetry is broken, we show that the ChernSimons state reduces to Jacobson's degenerate sector describing 1+1 dimensional propagating fermions with nonlocal interactions. The Hamiltonian admits a dual description which we realize in the simple BCS model of superconductivity. On one hand, Cooper pairs are interpreted as wormhole correlations at the de Sitter horizon; their number yields the de Sitter entropy. On the other hand, BCS is mapped into a deformed conformal field theory reproducing the structure of quantum spin networks. When area measurements are performed, Cooperpair insertions are activated on those edges of the spin network intersecting the given area, thus providing a description of quantum measurements in terms of excitations of a Fermi sea to superconducting levels. The cosmological constant problem is naturally addressed as a nonperturbative massgap effect of the true Fermiliquid vacuum. Comments: 45 pages, 1 figure; v2: discussion improved, version Superconducting loop quantum gravity and the cosmological constant Authors: Stephon H.S. Alexander, Gianluca Calcagni (Submitted on 26 Jun 2008 (v1), last revised 23 Feb 2009 (this version, v2)) Abstract: We argue that the cosmological constant is exponentially suppressed in a candidate ground state of loop quantum gravity as a nonperturbative effect of a holographic Fermiliquid theory living on a twodimensional spacetime. Ashtekar connection components, corresponding to degenerate gravitational configurations breaking large gauge invariance and CP symmetry, behave as composite fermions that condense as in BardeenCooperSchrieffer theory of superconductivity. Cooper pairs admit a description as wormholes on a de Sitter boundary. Comments: 10 pages; v2 matches the published version Subjects: High Energy Physics  Theory (hepth); Astrophysics (astroph); Superconductivity (condmat.suprcon); General Relativity and Quantum Cosmology (grqc) Journal reference: Physics Letters B 672 (2009) 386 DOI: 10.1016/j.physletb.2009.01.046 Report number: IGC08/65 Cite as: arXiv:0806.4382v2 [hepth] 



#3
Feb910, 12:10 AM

P: 716

http://arxiv.org/abs/1002.1462
Embedding the BilsonThompson model in an LQGlike framework Deepak Vaid (Submitted on 8 Feb 2010) We argue that the Quadratic Spinor Lagrangian approach allows us to approach the problem of forming a geometrical condensate of spinorial tetrads in a natural manner. This, along with considerations involving the discrete symmetries of lattice triangulations, lead us to discover that the quasiparticles of such a condensate are tetrahedra with braids attached to its faces and that these braid attachments correspond to the preons in BilsonThompson's model of elementary particles. These "spatoms" can then be put together in a tiling to form more complex structures which encode both geometry and matter in a natural manner. We conclude with some speculations on the relation between this picture and the computational universe hypothesis. 



#4
Feb1010, 03:05 PM

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Condensed matter physics, area laws & LQG?
I personally find this whole area very exciting. For example, the spin networks used in loop quantum gravity can be greatly generalized and potentially even realized in condensed matter systems called string net states. Furthermore, there are some exciting hints relating the way one computes black hole entropy in loop quantum gravity and entanglement entropy in the tensor network approach. There are also connections between the tensor network approach and AdS/CFT as Wen notes at the end of his slides.




#5
Feb1010, 08:10 PM

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P: 8,004

Also, what is the relationship between AdS/CFT and tensor networks? I remember reading a Horowitz and Polchinksi review that said AdS/CFT is an example of emergent gauge theory, which cited D'Adda 1978  whom Levin and Wen also cite, so was a little aware that AdS/CFT and string nets had a common descent  but haven't any understanding beyond that. Edit: Wow, I just saw you actually work on this stuff, unlike people like me who just read about it  very cool! 



#6
Feb1110, 11:16 AM

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So it looks like Jal and I had a related conversation a while ago in posts 6870 of his http://www.physicsforums.com/showthread.php?t=251509, with a quirky note by Michael Freedman pointing to papers by Brian Swingle and on to the entanglement entropy and holography.




#7
Feb1210, 08:42 AM

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#8
Feb1210, 08:46 AM

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#9
Feb1310, 11:52 AM

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#10
Feb1310, 03:23 PM

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SU(2) can be given but not chiral fermions. Is this true? It was deleted out as "speculative" research 



#11
Feb1610, 12:30 PM

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PS What kind of biology do you do? 



#12
Feb1610, 12:35 PM

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#13
Feb1610, 04:26 PM

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#14
Feb1710, 12:16 AM

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#15
Feb2210, 04:59 AM

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#16
Mar510, 01:15 AM

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#17
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#18
Mar510, 02:20 PM

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