A Unified Symmetry Classification of Many-Body Localized Phases
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866908793408847872 |
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| author | Wang, Yucheng |
| author_facet | Wang, Yucheng |
| contents | Anderson localization admits a complete symmetry classification given by the Altland-Zirnbauer (AZ) tenfold scheme, whereas an analogous framework for interacting many-body localization (MBL) has remained elusive. Here we develop a symmetry-based classification of static MBL phases formulated at the level of local integrals of motion (LIOMs). We show that a symmetry is compatible with stable MBL if and only if its action can be consistently represented within a quasi-local LIOM algebra, without enforcing extensive degeneracies or nonlocal operator mixing. This criterion sharply distinguishes symmetry classes: onsite Abelian symmetries are compatible with stable MBL and can host distinct symmetry-protected topological MBL phases, whereas continuous non-Abelian symmetries generically preclude stable MBL. By systematically combining AZ symmetries with additional onsite symmetries, we construct a complete classification table of MBL phases, identify stable, fragile, and unstable classes, and provide representative lattice realizations. Our results establish a unified and physically transparent framework for understanding symmetry constraints on MBL. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_20532 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A Unified Symmetry Classification of Many-Body Localized Phases Wang, Yucheng Disordered Systems and Neural Networks Quantum Gases Statistical Mechanics Quantum Physics Anderson localization admits a complete symmetry classification given by the Altland-Zirnbauer (AZ) tenfold scheme, whereas an analogous framework for interacting many-body localization (MBL) has remained elusive. Here we develop a symmetry-based classification of static MBL phases formulated at the level of local integrals of motion (LIOMs). We show that a symmetry is compatible with stable MBL if and only if its action can be consistently represented within a quasi-local LIOM algebra, without enforcing extensive degeneracies or nonlocal operator mixing. This criterion sharply distinguishes symmetry classes: onsite Abelian symmetries are compatible with stable MBL and can host distinct symmetry-protected topological MBL phases, whereas continuous non-Abelian symmetries generically preclude stable MBL. By systematically combining AZ symmetries with additional onsite symmetries, we construct a complete classification table of MBL phases, identify stable, fragile, and unstable classes, and provide representative lattice realizations. Our results establish a unified and physically transparent framework for understanding symmetry constraints on MBL. |
| title | A Unified Symmetry Classification of Many-Body Localized Phases |
| topic | Disordered Systems and Neural Networks Quantum Gases Statistical Mechanics Quantum Physics |
| url | https://arxiv.org/abs/2601.20532 |