Unified Symmetry Classification of Many-Body Localized Phases

Yucheng Wang

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arXiv · 2601.20532

Unified Symmetry Classification of Many-Body Localized Phases

Yucheng Wang

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Abstract

The Altland--Zirnbauer (AZ) tenfold way classifies disordered non-interacting systems by symmetry, but a unified symmetry classification of interacting many-body localized (MBL) phases has been lacking. Here we develop such a classification directly from the emergent local integrals of motion (LIOMs). Our scheme rests on two complementary criteria: whether a symmetry is compatible with a complete LIOM algebra, and whether it enforces many-body degeneracies. These criteria partition MBL phases into stable, fragile, symmetry-protected topological, and unstable classes, and unify AZ classes, onsite Abelian symmetries, and continuous non-Abelian symmetries within a single operator-algebraic framework. Our results provide a systematic foundation for understanding how symmetry constrains the stability and structure of MBL phases.

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cond-mat.dis-nn cond-mat.quant-gas cond-mat.stat-mech quant-ph

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Yucheng Wang. 2026-01-28. Unified Symmetry Classification of Many-Body Localized Phases. https://arxiv.org/abs/2601.20532

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