Fragmented ETH and Ensemble Inequivalence
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.
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BibTeX
@misc{sriram2026fragmented,
title = {{Fragmented ETH and Ensemble Inequivalence}},
author = {C. L. Sriram and Soumya Kanti Pal and Lea F. Santos},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2607.15350},
eprint = {2607.15350},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.15350},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Fragmented ETH and Ensemble Inequivalence
AU - C. L. Sriram
AU - Soumya Kanti Pal
AU - Lea F. Santos
PY - 2026
DA - 2026/09/03
PB - arXiv
DO - 10.48550/arxiv.2607.15350
UR - https://arxiv.org/abs/2607.15350
AB - 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.
ER -