Lieb-Schultz-Mattis Anomalies and Anomaly Matching
Abstract
Lieb-Schultz-Mattis (LSM) anomalies are powerful symmetry-based constraints on the correlation, entanglement and dynamics of quantum many-body systems. In this review, we discuss various LSM anomalies and anomaly matching. We start with a pedagogical introduction to these subjects in quantum spin chains, and then generalize the discussion to higher dimensions and other systems. Besides covering the topics related to the standard LSM anomalies, we also review LSM anomalies in disordered systems where the lattice symmetries are only preserved on average, fermionic systems, and systems where the symmetric short-range entangled states are possible but must be nontrivial symmetry-protected topological phases.
Cite
@article{arxiv.2604.00347,
title = {Lieb-Schultz-Mattis Anomalies and Anomaly Matching},
author = {Liujun Zou and Meng Cheng},
journal= {arXiv preprint arXiv:2604.00347},
year = {2026}
}
Comments
v1: Invited review for "Annual Review of Condensed Matter Physics". v2: The accepted version