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

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

doi:10.21468/SciPostPhys.11.2.024

SciPost Physics

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

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

SciPost Phys. 11, 024 (2021) · published 6 August 2021

doi: 10.21468/SciPostPhys.11.2.024
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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.

TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhys.11.2.024
TI  - Generalized Lieb-Schultz-Mattis theorem on bosonic symmetry protected topological phases
PY  - 2021/08/06
UR  - https://www.scipost.org/SciPostPhys.11.2.024
JF  - SciPost Physics
JA  - SciPost Phys.
VL  - 11
IS  - 2
SP  - 024
A1  - Jiang, Shenghan
AU  - Cheng, Meng
AU  - Qi, Yang
AU  - Lu, Yuan-Ming
AB  - 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.
ER  -

@Article{10.21468/SciPostPhys.11.2.024,
	title={{Generalized Lieb-Schultz-Mattis theorem on bosonic symmetry protected topological phases}},
	author={Shenghan Jiang and Meng Cheng and Yang Qi and Yuan-Ming Lu},
	journal={SciPost Phys.},
	volume={11},
	pages={024},
	year={2021},
	publisher={SciPost},
	doi={10.21468/SciPostPhys.11.2.024},
	url={https://scipost.org/10.21468/SciPostPhys.11.2.024},
}

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¹ ² Shenghan Jiang,
³ Meng Cheng,
⁴ ⁵ Yang Qi,
⁶ Yuan-Ming Lu

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