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This research establishes a unified operator-algebraic framework to classify interacting many-body localized (MBL) phases, addressing a significant gap in the symmetry classification of disordered quantum systems. By deriving categories from emergent local integrals of motion, the study integrates various existing symmetries into a single theoretical structure that defines phase stability and topology. This foundational work advances our understanding of how symmetry constraints govern the structural integrity of complex localized states in quantum matter.
Unified Symmetry Classification of Many-Body Localized Phases
arXiv:2601.20532v2 Announce Type: replace-cross 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.
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.
Disordered Systems and Neural Networks (cond-mat.dis-nn); Quantum Gases (cond-mat.quant-gas); Statistical Mechanics (cond-mat.stat-mech); Quantum Physics (quant-ph)
arXiv:2601.20532 [cond-mat.dis-nn]
(or arXiv:2601.20532v2 [cond-mat.dis-nn] for this version)
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