2026-05-25 京都大学
通常の対称性（左）では操作は逆操作によって元に戻る。一方、本研究で見出された非可逆対称性（右）では逆操作が単純には存在せず、状態が複数に分かれる。作成：戎 弘実
＜関連情報＞
- https://www.kyoto-u.ac.jp/ja/research-news/2026-05-25
- https://journals.aps.org/prb/abstract/10.1103/qmcw-dbrs
Lieb–Schultz–Mattis アノマリーからの非可逆並進 Noninvertible translation from Lieb-Schultz-Mattis anomaly
Tsubasa Oishi, Takuma Saito, and Hiromi Ebisu
Physical Review B Published: 21 May, 2026
DOI: https://doi.org/10.1103/qmcw-dbrs
Abstract
Symmetry provides powerful nonperturbative constraints in quantum many-body systems. A prominent example is the Lieb-Schultz-Mattis (LSM) anomaly—a mixed ‘t Hooft anomaly between internal and translational symmetries that forbids a trivial symmetric gapped phase. In this work, we investigate lattice translation operators in systems with an LSM anomaly. We construct explicit lattice models in two and three spatial dimensions and show that, after gauging the full internal symmetry, translation becomes noninvertible and fuses into defects of the internal symmetry. The result is supported by the anomaly inflow in view of topological field theory. Our work extends earlier one-dimensional observations to a unified higher-dimensional framework and clarifies their origin in mixed anomalies and higher-group structures, highlighting a coherent interplay between internal and crystalline symmetries.
