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Title: Determining topological order from infinite projected entangled pair states

Journal Article · · Physical Review B
ORCiD logo [1];  [1];  [2]; ORCiD logo [3]
  1. Jagiellonian Univ., Krakow (Poland)
  2. Perimeter Inst. for Theoretical Physics, Waterloo, ON (Canada); The Moonshot Factory, Mountain View, CA (United States)
  3. Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
+ Show Author Affiliations

In this work, we present a method of extracting information about the topological order from the ground state of a strongly correlated two-dimensional system computed with the infinite projected entangled pair state (iPEPS). For topologically ordered systems, the iPEPS wrapped on a torus becomes a superposition of degenerate, locally indistinguishable ground states. Projectors in the form of infinite matrix product operators onto states with well-defined anyon flux are used to compute topological S and T matrices (encoding mutual and self-statistics of emergent anyons). The algorithm is shown to be robust against a perturbation driving string-net toric code across a phase transition to a ferromagnetic phase. Our approach provides accurate results near quantum phase transition, where the correlation length is prohibitively large for other numerical methods. Moreover, we used numerically optimized iPEPS describing the ground state of the Kitaev honeycomb model in the toric code phase and obtained topological data in excellent agreement with theoretical prediction.

Research Organization:
Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
Sponsoring Organization:
Narodowe Centrum Nauki (NCN); Polish Ministry of Science and Education; USDOE Laboratory Directed Research and Development (LDRD) Program; USDOE Office of Science (SC), Basic Energy Sciences (BES). Materials Sciences & Engineering Division
Grant/Contract Number:
89233218CNA000001
OSTI ID:
1726174
Report Number(s):
LA-UR--19-29100
Journal Information:
Physical Review B, Journal Name: Physical Review B Journal Issue: 4 Vol. 101; ISSN 2469-9950
Publisher:
American Physical Society (APS)Copyright Statement
Country of Publication:
United States
Language:
English

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A theory of 2+1D bosonic topological orders text January 2015
Haldane-Hubbard Mott Insulator: From Tetrahedral Spin Crystal to Chiral Spin Liquid text January 2015
Space group symmetry fractionalization in a chiral kagome Heisenberg antiferromagnet text January 2015
Anyons and matrix product operator algebras text January 2015
Variational optimization with infinite projected entangled-pair states text January 2016
Symmetry fractionalization in the topological phase of the spin-$\frac{1}{2}$ $J_1$-$J_2$ triangular Heisenberg model text January 2016
Signatures of Dirac cones in a DMRG study of the Kagome Heisenberg model text January 2016
Realizing and Adiabatically Preparing Bosonic Integer and Fractional Quantum Hall states in Optical Lattices text January 2017
Nature of continuous phase transitions in interacting topological insulators text January 2017
Tunning topological phase and quantum anomalous Hall effect by interaction in quadratic band touching systems text January 2018
String-net condensation: A physical mechanism for topological phases text January 2004
Anyons in an exactly solved model and beyond text January 2005
Classical simulation of infinite-size quantum lattice systems in two spatial dimensions text January 2007
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36 MATERIALS SCIENCE
Topological phases of matter
projected entangled pair states
tensor network methods