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Generalized Lieb-Schultz-Mattis theorem on bosonic symmetry protected topological phases

by Shenghan Jiang, Meng Cheng, Yang Qi, Yuan-Ming Lu

Submission summary

As Contributors: Shenghan Jiang
Arxiv Link: https://arxiv.org/abs/1907.08596v1
Date submitted: 2020-01-28
Submitted by: Jiang, Shenghan
Submitted to: SciPost Physics
Discipline: Physics
Subject area: Condensed Matter Physics - Theory
Approach: Theoretical

Abstract

We propose and prove a family of generalized Lieb-Schultz-Mattis (LSM) theorems for symmetry protected topological (SPT) phases on boson/spin models in any dimensions. The "conventional" LSM theorem, applicable to e.g. any translation invariant system with an odd number of spin-1/2 particles per unit cell, forbids a symmetric short-range-entangled ground state in such a system. Here we focus on systems with no LSM anomaly, where global/crystalline symmetries and fractional spins within the unit cell ensure that any symmetric SRE ground state must be a nontrivial SPT phase with anomalous boundary excitations. Depending on models, they can be either strong or "higher-order" crystalline SPT phases, characterized by nontrivial surface/hinge/corner states. Furthermore, given the symmetry group and the spatial assignment of fractional spins, we are able to determine all possible SPT phases for a symmetric ground state, using the real space construction for SPT phases based on the spectral sequence of cohomology theory. We provide examples in one, two and three spatial dimensions, and discuss possible physical realization of these SPT phases based on condensation of topological excitations in fractionalized phases.

Current status:
Editor-in-charge assigned


Submission & Refereeing History

Submission 1907.08596v1 on 28 January 2020

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