Anomaly manifestation of Lieb-Schultz-Mattis theorem and topological phases

Gil Young Cho, Chang-Tse Hsieh, and Shinsei Ryu
Phys. Rev. B 96, 195105 – Published 2 November 2017

Abstract

The Lieb-Schultz-Mattis (LSM) theorem dictates that emergent low-energy states from a lattice model cannot be a trivial symmetric insulator if the filling per unit cell is not integral and if the lattice translation symmetry and particle number conservation are strictly imposed. In this paper, we compare the one-dimensional gapless states enforced by the LSM theorem and the boundaries of one-higher dimensional strong symmetry-protected topological (SPT) phases from the perspective of quantum anomalies. We first note that they can both be described by the same low-energy effective field theory with the same effective symmetry realizations on low-energy modes, wherein non-on-site lattice translation symmetry is encoded as if it were an internal symmetry. In spite of the identical form of the low-energy effective field theories, we show that the quantum anomalies of the theories play different roles in the two systems. In particular, we find that the chiral anomaly is equivalent to the LSM theorem, whereas there is another anomaly that is not related to the LSM theorem but is intrinsic to the SPT states. As an application, we extend the conventional LSM theorem to multiple-charge multiple-species problems and construct several exotic symmetric insulators. We also find that the (3+1)d chiral anomaly provides only the perturbative stability of the gaplessness local in the parameter space.

  • Figure
  • Received 13 August 2017

DOI:https://doi.org/10.1103/PhysRevB.96.195105

©2017 American Physical Society

Physics Subject Headings (PhySH)

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Gil Young Cho1,2, Chang-Tse Hsieh3, and Shinsei Ryu4

  • 1School of Physics, Korea Institute for Advanced Study, Seoul 02455, Korea
  • 2Department of Physics, Korea Advanced Institute of Science and Technology, Daejeon 305-701, Korea
  • 3Department of Physics, University of Illinois, 1110 West Green Street, Urbana, Illinois 61801-3080, USA
  • 4James Franck Institute and Kadanoff Center for Theoretical Physics, University of Chicago, Chicago, Illinois 60637, USA

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Issue

Vol. 96, Iss. 19 — 15 November 2017

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