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This research advances fundamental quantum statistical mechanics by introducing the fragmented eigenstate thermalization hypothesis (fETH), which describes how Hilbert space fragmentation leads to slow, two-stage equilibration in systems with long-range interactions. The study provides analytical tools for calculating prethermal plateau timescales and resolves ensemble inequivalence through a band-resolved framework that does not rely on phase transitions. These insights are critical for understanding thermalization limits in quantum simulators and future fault-tolerant quantum processors where ergodicity may be broken by specific interaction structures.
Fragmented ETH: Prethermalization, Timescales, and Ensemble Inequivalence
arXiv:2607.15350v1 Announce Type: cross Abstract: We investigate how finite quantum systems with strong long-range interactions approach thermal equilibrium. Nearly conserved quantities inherited from the fully connected limit fragment the Hilbert space and give rise to a many-body spectrum split into energy bands. As a result, equilibration becomes anomalously slow and proceeds through long-lived prethermal plateaus. This two-stage equilibration process is, however, not universal. We uncover the mechanism that determines which observables and initial states exhibit, or evade, prethermal plateaus. We also develop a perturbative theory that provides analytical expressions for both the height of the prethermal plateau and its timescale. Despite the lack 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 direct 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 to a broad class of Hamiltonians exhibiting Hilbert-space fragmentation.
Abstract:We investigate how finite quantum systems with strong long-range interactions approach thermal equilibrium. Nearly conserved quantities inherited from the fully connected limit fragment the Hilbert space and give rise to a many-body spectrum split into energy bands. As a result, equilibration becomes anomalously slow and proceeds through long-lived prethermal plateaus. This two-stage equilibration process is, however, not universal. We uncover the mechanism that determines which observables and initial states exhibit, or evade, prethermal plateaus. We also develop a perturbative theory that provides analytical expressions for both the height of the prethermal plateau and its timescale. Despite the lack 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 direct 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 to a broad class of Hamiltonians exhibiting Hilbert-space fragmentation.
Statistical Mechanics (cond-mat.stat-mech); Quantum Physics (quant-ph)
arXiv:2607.15350 [cond-mat.stat-mech]
(or arXiv:2607.15350v1 [cond-mat.stat-mech] for this version)
https://doi.org/10.48550/arXiv.2607.15350 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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