Bulletin of the American Physical Society
APS March Meeting 2018
Monday–Friday, March 5–9, 2018; Los Angeles, California
Session P42: Recent Progress in Tensor Network Methods and ApplicationsInvited

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Sponsoring Units: DCOMP DCMP Chair: Edwin Stoudenmire, University of California  Irvine Room: LACC 502B 
Wednesday, March 7, 2018 2:30PM  3:06PM 
P42.00001: Hyperinvariant tensor networks and holography Invited Speaker: Glen Evenbly I will discuss a recent proposal of a new class of tensor network state as a model for the AdS/CFT correspondence and holography (Phys. Rev. Lett. 119, 141602). This class is demonstrated to retain key features of the multiscale entanglement renormalization ansatz (MERA), in that they describe quantum states with algebraic correlation functions, have free variational parameters, and are efficiently contractible. Yet, unlike MERA, they are built according to a uniform tiling of hyperbolic space, without inherent directionality or preferred locations in the holographic bulk, and thus circumvent key arguments made against the MERA as a model for AdS/CFT. Novel holographic features of this tensor network class will be examined, such as an equivalence between the causal cone C[R] and the entanglement wedge E[R] of connected boundary regions R. 
Wednesday, March 7, 2018 3:06PM  3:42PM 
P42.00002: Using Tensor Network States for Lattice Gauge Theories Invited Speaker: Mari Bañuls , Krzysztof Cichy , Ignacio Cirac , Karl Jansen , Stefan Kühn Tensor Network (TN) potential for the study of strongly correlated systems extends far beyond their original realm of application in the context of condensed matter problems. One particular scenario where TN techniques should be helpful is that of Lattice Gauge Theories in their Hamiltonian version. While the dimensions and sizes of the systems amenable to TNS studies are still far from those achievable by traditional Monte Carlo simulations, Tensor Networks can be readily used for problems which more standard techniques cannot easily tackle, due to the appearance of a sign problem, such as in the presence of a chemical potential, or outofequilibrium dynamics. 
Wednesday, March 7, 2018 3:42PM  4:18PM 
P42.00003: Post Matrix Product State Methods: from lowenergy dynamics to thermalization Invited Speaker: Jutho Haegeman , Laurens Vanderstraeten , Frank Verstraete In this talk, I will review the concept of socalled "Post Matrix Product State (MPS) methods", i.e. algorithms based on the geometrical concept of the MPS manifold and its tangent space. The MPS tange space appears naturally when applying the DiracFrenkel timedependent variational principle (TDVP) to the set of MPS, with provides an alternative algorithm to study time evolution and is becoming increasingly more popular, because it can easily deal with longrange interactions and does not suffer from some of the drawbacks of methods like the TimeEvolving Block Decimation. However, time evolution still leads to unbounded growth of entanglement, and when interested in the lowenergy dynamics, the MPS tangent space and its extensions provides alternative methods to target e.g. the elementary quasiparticle excitations on top of the strongly correlated MPS ground state, and to compute their dispersion relation, their scattering matrix, and their contribution to spectral functions. More recently, the symplectic properties of the TDVP evolution have also made it a potential candidate to transform the unitary dynamics of closed quantum systems into an effective chaotic semiclassical dynamics that can be used to study thermalization. 
Wednesday, March 7, 2018 4:18PM  4:54PM 
P42.00004: Iterative CompressionDecimation Scheme for Tensor Network Optimization Invited Speaker: Zhicheng Yang , Stefanos Kourtis , Claudio Chamon , Eduardo Mucciolo , Andrei Ruckenstein Tensor network methods are now a widely used tool in several branches of theoretical physics, particularly in the area of strongly correlated systems. The main obstacle in employing these techniques to solve hard (classical or quantum) strongly correlated problems is the need to fully contract a tensor network to obtain physical quantities of interest, such as observables or partition functions. Several elaborate strategies to perform the tensor network contraction have been developed in the past few years. However, important classes of systems, such as systems lacking translational invariance or systems with arbitrary boundary conditions, have so far remained mostly outside the scope of tensor network techniques. In this talk, I will describe a simple yet powerful scheme, called iterative compressiondecimation (ICD), to perform full tensor network contractions in systems with disorder and / or arbitrary boundaries [1]. The algorithm iteratively removes redundancies in tensor entries due to either short range entanglement or constrains imposed locally and, more importantly, globally at the boundary. I will demonstrate the efficiency of the method in solving hard computational problems and in simulating quantum dynamics via a 1+1D tensor network representation of the history of a onedimensional quantum state. 
Wednesday, March 7, 2018 4:54PM  5:30PM 
P42.00005: Continuous matrix product density operators for quantum fields at finite temperature Invited Speaker: Julian Rincon This abstract not available. 
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