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Title:
A disordered spin chain with on-site finite non-Abelian symmetry---a case study of its eigenstate phases
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Abstract:
Many-body localization (MBL) has emerged as a generic class of interacting and disordered isolated systems. A recent work by Potter and Vasseur shows that MBL phases are not compatible with non-Abelian symmetry. We develop a general formalism based on standard group theory to construct local spin Hamiltonians invariant under any on-site symmetry. We then specialize to the case of the simplest non-Abelian group, S3, and study a particular two-parameter spin-1 chain with S3 symmetry. We observe a thermal phase and a many-body localized phase with a spontaneous symmetry breaking (SSB) from S3 to Z3 symmetry. We diagnose these phases using full entanglement distributions and level statistics, as well as a spin-glass diagnostic specialized to detect spontaneous breaking of the S3 symmetry. Our observed phases are consistent with the possibilities outlined by Potter and Vasseur, but we also find an intermediate region between the thermal and MBL+SSB regions where full S3 symmetry exists.
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