Geometric approach to Lieb-Schultz-Mattis theorem without translation symmetry under inversion or rotation symmetry

• URL: http://arxiv.org/abs/2110.08819v2
• Date: Wed, 20 Jul 2022 06:55:54 GMT
• Title: Geometric approach to Lieb-Schultz-Mattis theorem without translation symmetry under inversion or rotation symmetry
• Authors: Yuan Yao and Akira Furusaki
• Abstract summary: We find that any inversion-symmetric spin system possesses a doubly degenerate spectrum when it hosts a half-integer spin at the inversion-symmetric point. We argue that these degeneracies imply that a symmetric unique gapped ground state that is smoothly connected to product states is forbidden in the original untwisted systems.
• Score: 6.737752058029072
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We propose a geometric {approach to Lieb-Schultz-Mattis theorem for} quantum many-body systems with discrete spin-rotation symmetries and lattice inversion or rotation symmetry, but without translation symmetry assumed. Under symmetry-twisting on a $(d-1)$-dimensional plane, we find that any $d$-dimensional inversion-symmetric spin system possesses a doubly degenerate spectrum when it hosts a half-integer spin at the inversion-symmetric point. We also show that any rotation-symmetric generalized spin model with a projective representation at the rotation center has a similar degeneracy under symmetry-twisting. We argue that these degeneracies imply that {a unique symmetric gapped ground state that is smoothly connected to product states} is forbidden in the original untwisted systems -- generalized inversional/rotational Lieb-Schultz-Mattis theorems without lattice translation symmetry imposed. The traditional Lieb-Schultz-Mattis theorems with translations also fit in the proposed framework.

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