Detecting and identifying two-dimensional symmetry-protected topological, symmetry-breaking, and intrinsic topological phases with modular matrices via tensor-network methods

Ching-Yu Huang and Tzu-Chieh Wei
Phys. Rev. B 93, 155163 – Published 28 April 2016

Abstract

Symmetry-protected topological (SPT) phases exhibit nontrivial order if symmetry is respected but are adiabatically connected to the trivial product phase if symmetry is not respected. However, unlike the symmetry-breaking phase, there is no local order parameter for SPT phases. Here we employ a tensor-network method to compute the topological invariants characterized by the simulated modular S and T matrices to study transitions in a few families of two-dimensional (2D) wave functions which are ZN (N=2and3) symmetric. We find that in addition to the topologically ordered phases, the modular matrices can be used to identify nontrivial SPT phases and detect transitions between different SPT phases as well as between symmetric and symmetry-breaking phases. Therefore modular matrices can be used to characterize various types of gapped phases in a unifying way.

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  • Received 28 December 2015
  • Revised 6 April 2016

DOI:https://doi.org/10.1103/PhysRevB.93.155163

©2016 American Physical Society

Physics Subject Headings (PhySH)

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Ching-Yu Huang and Tzu-Chieh Wei

  • C. N. Yang Institute for Theoretical Physics and Department of Physics and Astronomy, State University of New York at Stony Brook, New York 11794-3840, United States

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Issue

Vol. 93, Iss. 15 — 15 April 2016

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