Lieb-Schultz-Mattis Anomalies and Anomaly Matching
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866913072370679808 |
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| author | Zou, Liujun Cheng, Meng |
| author_facet | Zou, Liujun Cheng, Meng |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2604_00347 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Lieb-Schultz-Mattis Anomalies and Anomaly Matching Zou, Liujun Cheng, Meng Strongly Correlated Electrons Quantum Gases High Energy Physics - Theory Mathematical Physics 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. |
| title | Lieb-Schultz-Mattis Anomalies and Anomaly Matching |
| topic | Strongly Correlated Electrons Quantum Gases High Energy Physics - Theory Mathematical Physics |
| url | https://arxiv.org/abs/2604.00347 |