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

Jiang, Shenghan and Cheng, Meng and Qi, Yang and Lu, Yuan-Ming (2021) Generalized Lieb-Schultz-Mattis theorem on bosonic symmetry protected topological phases. SciPost Physics, 11 (2). Art. No. 24. ISSN 2542-4653. doi:10.21468/scipostphys.11.2.024.

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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.

Item Type:Article
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URLURL TypeDescription Paper
Qi, Yang0000-0003-0678-9770
Lu, Yuan-Ming0000-0001-6275-739X
Additional Information:© 2021 Jiang et al. This work is licensed under the Creative Commons Attribution 4.0 International License. Published by the SciPost Foundation. Received 28-01-2020; Accepted 04-08-2021; Published 06-08-2021. Shenghan thanks Lesik Motrunich, Xie Chen, Xu Yang, and Peng Ye for helpful discussions on 3D SPT phase and monopole condensation. This work is supported by the Institute for Quantum Information and Matter, an NSF Physics Frontiers Center, with support of the Gordon and Betty Moore Foundation (SJ), NSF under award number DMR-1653769 (YML) and DMR-1846109 (MC). MC is also supported by Alfred P. Sloan Research Fellowship. YQ acknowledges support from Minstry of Science and Technology of China under grant numbers 2015CB921700, and from National Science Foundation of China under grant number 11874115. This work was performed in part at Aspen Center for Physics, which is supported by National Science Foundation grant PHY-1607611. MC and YML also thanks hospitality of CMSA program “Topological Aspects of Condensed Matter” at Harvard University, where a part of this work was performed. Note added: We would like to draw the readers’ attention to a related work by Dominic Else and Ryan Thorngren, to appear in the same arXiv posting.
Group:Institute for Quantum Information and Matter
Funding AgencyGrant Number
Institute for Quantum Information and Matter (IQIM)UNSPECIFIED
Gordon and Betty Moore FoundationUNSPECIFIED
Alfred P. Sloan FoundationUNSPECIFIED
Ministry of Science and Technology (Taipei)2015CB921700
National Natural Science Foundation of China11874115
Issue or Number:2
Record Number:CaltechAUTHORS:20211116-155504417
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:111889
Deposited By: Tony Diaz
Deposited On:16 Nov 2021 17:00
Last Modified:16 Nov 2021 17:00

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