• Open Access

Anomaly Matching and Symmetry-Protected Critical Phases in SU(N) Spin Systems in 1+1 Dimensions

Yuan Yao, Chang-Tse Hsieh, and Masaki Oshikawa
Phys. Rev. Lett. 123, 180201 – Published 31 October 2019
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Abstract

We study (1+1)-dimensional SU(N) spin systems in the presence of global SU(N) rotation and lattice translation symmetries. Knowing the mixed anomaly of the two symmetries at low energy, we identify, by the anomaly matching argument, a topological index for the spin model—the total number of Young-tableau boxes of spins per unit cell modulo N—characterizing the “ingappability” of the system. A nontrivial index implies either a ground-state degeneracy in a gapped phase, which can be thought of as a field-theory version of the Lieb-Schultz-Mattis theorem, or a restriction of the possible universality classes in a critical phase, regarded as the symmetry-protected critical phases. As an example of the latter case, we show that only a class of SU(N) Wess-Zumino-Witten theories can be realized in the low-energy limit of the given lattice model in the presence of the symmetries. Similar constraints also apply when a higher global symmetry emerges in the model with a lower symmetry. Our results agree with several examples known in previous studies of SU(N) models, and predict a general constraint on the structure factor which is measurable in experiments.

  • Received 13 June 2018
  • Revised 10 September 2019

DOI:https://doi.org/10.1103/PhysRevLett.123.180201

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

© 2019 American Physical Society

Physics Subject Headings (PhySH)

Particles & FieldsStatistical Physics & ThermodynamicsCondensed Matter, Materials & Applied Physics

Authors & Affiliations

Yuan Yao1,*, Chang-Tse Hsieh2,1,*, and Masaki Oshikawa1,2

  • 1Institute for Solid State Physics, The University of Tokyo, Kashiwa, Chiba 277-8581, Japan
  • 2Kavli Institute for the Physics and Mathematics of the Universe (WPI), The University of Tokyo Institutes for Advanced Study, The University of Tokyo, Kashiwa, Chiba 277-8583, Japan

  • *These authors contributed equally to this work.

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Issue

Vol. 123, Iss. 18 — 1 November 2019

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