For systems with projective symmetry representations, the paper proposes a modified ETH and shows that charged operators with symmetry-supplied charges thermalize to a generalized Gibbs ensemble, not the ordinary Gibbs ensemble.
Eigenstate thermalization within isolated spin-chain systems,
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Eigenstate Thermalization Hypothesis with projective representation
For systems with projective symmetry representations, the paper proposes a modified ETH and shows that charged operators with symmetry-supplied charges thermalize to a generalized Gibbs ensemble, not the ordinary Gibbs ensemble.