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This research introduces the fragmented eigenstate thermalization hypothesis (fETH), a framework describing how quantum systems with long-range interactions organize into weakly coupled energy bands rather than global ergodic states. By demonstrating that microcanonical and canonical ensembles behave differently within these bands, the study resolves ensemble inequivalence without relying on traditional phase transitions. These findings advance fundamental understanding of thermalization in finite quantum systems near permutation-symmetric limits.
Fragmented ETH and Ensemble Inequivalence
arXiv:2607.15350v2 Announce Type: replace-cross Abstract: We investigate thermalization in finite quantum systems with strong long-range interactions. Nearly conserved quantities inherited from the fully connected limit organize the Hilbert space into weakly coupled sectors and split the many-body spectrum into energy bands. Despite the resulting breakdown of global ergodicity, quantum chaos develops within individual energy bands, enabling the definition of microcanonical ensembles within the bands. This supports a band-resolved formulation of thermalization, which we term fragmented eigenstate thermalization hypothesis (fETH). Unlike conventional ETH, finite-size scaling in fETH obeys a symmetry-imposed selection rule that restricts which system sizes can be compared. This band-resolved description has consequences for equilibrium statistical mechanics. While microcanonical ensembles remain confined to a single band, canonical ensembles mix different bands. This mismatch explains ensemble inequivalence without invoking equilibrium phase transitions. Our results apply broadly to Hamiltonians near a fully permutation-symmetric limit.
Abstract:We investigate thermalization in finite quantum systems with strong long-range interactions. Nearly conserved quantities inherited from the fully connected limit organize the Hilbert space into weakly coupled sectors and split the many-body spectrum into energy bands. Despite the resulting breakdown of global ergodicity, quantum chaos develops within individual energy bands, enabling the definition of microcanonical ensembles within the bands. This supports a band-resolved formulation of thermalization, which we term fragmented eigenstate thermalization hypothesis (fETH). Unlike conventional ETH, finite-size scaling in fETH obeys a symmetry-imposed selection rule that restricts which system sizes can be compared. This band-resolved description has consequences for equilibrium statistical mechanics. While microcanonical ensembles remain confined to a single band, canonical ensembles mix different bands. This mismatch explains ensemble inequivalence without invoking equilibrium phase transitions. Our results apply broadly to Hamiltonians near a fully permutation-symmetric limit.
14 pages, 6 figures; This second version of the manuscript contains only the static part of the original paper, covering fETH and ensemble inequivalence. Prethermalization is now discussed in arXiv:2609.01606
Statistical Mechanics (cond-mat.stat-mech); Quantum Physics (quant-ph)
arXiv:2607.15350 [cond-mat.stat-mech]
(or arXiv:2607.15350v2 [cond-mat.stat-mech] for this version)
Full text under the publisher's open licence · 182 words
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