Lieb-Schultz-Mattis theorems for symmetry-protected topological phases

IF 3 3区 物理与天体物理 Q2 PHYSICS, MULTIDISCIPLINARY Annals of Physics Pub Date : 2024-09-23 DOI:10.1016/j.aop.2024.169806
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Abstract

The Lieb-Schultz-Mattis (LSM) theorem and its generalizations are a class of powerful no-go theorems that rule out any short-range-entangled (SRE) symmetric ground state irrespective of the specific Hamiltonian, based only on certain microscopic inputs, such as symmetries and particle filling numbers. In this work, we introduce and provide physical arguments for a new class of LSM-type theorems, where any symmetry-allowed SRE ground state must be a symmetry-protected topological (SPT) phase with robust gapless edge states, such as topological insulators and superconductors. The key ingredient is to replace the lattice translation symmetry in usual LSM theorems by the magnetic translation symmetry. These theorems provide new insights into realistic models and experimental realizations of SPT phases in interacting bosons and fermions.
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对称保护拓扑相的利布-舒尔茨-马蒂斯定理
Lieb-Schultz-Mattis(LSM)定理及其广义是一类强大的禁区定理,它仅基于某些微观输入,如对称性和粒子填充数,就能排除任何短程纠缠(SRE)对称基态,而不管具体的哈密顿。在这项工作中,我们引入了一类新的 LSM 型定理并提供了物理论证,其中任何对称允许的 SRE 基态必须是具有稳健无间隙边缘态的对称保护拓扑(SPT)相,如拓扑绝缘体和超导体。其关键要素是用磁平移对称性取代通常 LSM 理论中的晶格平移对称性。这些定理为相互作用玻色子和费米子中 SPT 相的现实模型和实验实现提供了新的见解。
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来源期刊
Annals of Physics
Annals of Physics 物理-物理:综合
CiteScore
5.30
自引率
3.30%
发文量
211
审稿时长
47 days
期刊介绍: Annals of Physics presents original work in all areas of basic theoretic physics research. Ideas are developed and fully explored, and thorough treatment is given to first principles and ultimate applications. Annals of Physics emphasizes clarity and intelligibility in the articles it publishes, thus making them as accessible as possible. Readers familiar with recent developments in the field are provided with sufficient detail and background to follow the arguments and understand their significance. The Editors of the journal cover all fields of theoretical physics. Articles published in the journal are typically longer than 20 pages.
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