Topological field theory and matrix product states

Anton Kapustin, Alex Turzillo, and Minyoung You
Phys. Rev. B 96, 075125 – Published 14 August 2017

Abstract

It is believed that most (perhaps all) gapped phases of matter can be described at long distances by topological quantum field theory (TQFT). On the other hand, it has been rigorously established that in 1+1d ground states of gapped Hamiltonians can be approximated by matrix product states (MPS). We show that the state-sum construction of 2d TQFT naturally leads to MPS in their standard form. In the case of systems with a global symmetry G, this leads to a classification of gapped phases in 1+1d in terms of Morita-equivalence classes of G-equivariant algebras. Nonuniqueness of the MPS representation is traced to the freedom of choosing an algebra in a particular Morita class. In the case of short-range entangled phases, we recover the group cohomology classification of SPT phases.

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  • Received 6 June 2017

DOI:https://doi.org/10.1103/PhysRevB.96.075125

©2017 American Physical Society

Physics Subject Headings (PhySH)

Condensed Matter, Materials & Applied PhysicsParticles & Fields

Authors & Affiliations

Anton Kapustin, Alex Turzillo, and Minyoung You

  • California Institute of Technology, 1200 E California Blvd, Pasadena, California 91125, USA

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Issue

Vol. 96, Iss. 7 — 15 August 2017

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