University of Connecticut Perturbative Theory Predicts Plateau Height & Timescale

A perturbative theory developed by C. L. Sriram and Lea F. Santos at the University of Connecticut, and Soumya Kanti Pal at the Tata Institute of Fundamental Research, now provides analytical expressions for both the height and timescale of how long it takes for strongly interacting quantum systems to approach equilibrium, a calculation previously beyond reach. Researchers found that nearly conserved quantities fragment the system’s quantum behavior, leading to a two-stage equilibration process with long-lived prethermal plateaus. Unlike conventional eigenstate thermalization hypothesis, the team’s fragmented eigenstate thermalization hypothesis (fETH) obeys a symmetry-imposed selection rule that restricts which system sizes can be compared. This band-resolved description also explains ensemble inequivalence without invoking equilibrium phase transitions, offering a new perspective on statistical mechanics for systems exhibiting Hilbert-space fragmentation.

Long-Range Interactions and Hilbert Space Fragmentation

The structure of quantum chaos is being clarified by discoveries revealing how long-range interactions fundamentally alter the path to thermal equilibrium. Research led by C. L. Sriram at the University of Connecticut, in collaboration with Soumya Kanti Pal of the Tata Institute of Fundamental Research and Lea F. Santos at the University of Connecticut, demonstrates that systems exhibiting strong, long-range interactions do not simply scramble towards disorder as previously understood, but instead navigate a fragmented quantum landscape. The team’s work, dated July 16, 2026, details how these interactions split the system’s quantum states into distinct energy bands, dramatically slowing the approach to equilibrium. This fragmentation is not a roadblock to thermalization; instead, the study reveals that finite-size scaling in the team’s fragmented eigenstate thermalization hypothesis (fETH) obeys a symmetry-imposed selection rule that restricts which system sizes can be compared. The team’s analysis extends beyond dynamics, offering insights into statistical mechanics.

The work highlights a mismatch between microcanonical and canonical ensembles, a result of the band structure, explaining ensemble inequivalence without invoking equilibrium phase transitions. This proposes a mechanism that avoids needing to invoke equilibrium phase transitions as an explanation for discrepancies in ensemble predictions. “Our results apply to a broad class of Hamiltonians exhibiting Hilbert-space fragmentation,” the researchers state, suggesting the broad applicability of their findings to diverse quantum systems, including those realized in trapped ion and Rydberg atom experiments.

The study of non-equilibrium dynamics in strongly interacting quantum systems has revealed a surprising two-stage approach to thermalization, often marked by extended plateaus before systems ultimately reach equilibrium. However, the team’s analysis reveals that this is a natural consequence of the symmetry-imposed selection rule that restricts which system sizes can be compared. This constraint arises from the fragmentation of the Hilbert space due to the strong, long-range interactions, splitting the many-body spectrum into distinct energy bands. The work demonstrates that while global ergodicity is lost, quantum chaos still develops within these individual bands, supporting a band-resolved approach to understanding thermalization. The researchers also note that a mismatch between microcanonical and canonical ensembles arises as a result of the band structure. “While the appropriate microcanonical ensemble is confined to a single energy band, the canonical ensemble samples states from different bands,” they write, highlighting the origin of the differing predictions. This band-resolved perspective offers a new microscopic mechanism for explaining ensemble inequivalence without invoking equilibrium phase transitions, potentially reshaping our understanding of equilibrium statistical mechanics.

This analytical framework builds upon observations of long-lived prethermal plateaus, where systems temporarily stall before fully equilibrating, a phenomenon seen in experiments with trapped ions and Rydberg atoms. However, this analysis reveals that conventional approaches to understanding thermalization may need refinement. The team’s “fragmented eigenstate thermalization hypothesis (fETH)” defines a term, rather than introducing a new hypothesis, and unlike conventional ETH, finite-size scaling in fETH obeys a symmetry-imposed selection rule that restricts which system sizes can be compared. The implications extend beyond simply understanding if thermalization occurs, but how it occurs within specific system parameters. The researchers have identified that a band structure explains ensemble inequivalence without invoking equilibrium phase transitions, and that this explains discrepancies between microcanonical and canonical ensembles, statistical methods used to describe equilibrium states. They demonstrate that the mismatch arises because microcanonical ensembles remain confined to single energy bands, while canonical ensembles sample across multiple bands.

Conventional wisdom suggests that quantum systems, given enough time, will smoothly transition to thermal equilibrium; however, recent work challenges this notion by demonstrating that strong, long-range interactions can dramatically alter this process, creating a fragmented energy landscape. This fragmentation doesn’t halt thermalization entirely, but rather confines it within individual bands, leading to a band-resolved understanding of the process. This work acknowledges that finite-size scaling obeys a symmetry-imposed selection rule that restricts which system sizes can be compared, and is a natural consequence of this rule. The researchers find that a mismatch between microcanonical and canonical ensembles arises from this band structure.

This limitation stems from the unique structure of these systems, where strong, long-range interactions create a fragmented Hilbert space, essentially splitting the system into distinct, isolated sectors. While conventional ETH assumes a smooth scaling with system size, fETH obeys a symmetry-imposed selection rule that restricts which system sizes can be compared. This work highlights a natural consequence of the symmetry-imposed selection rule, and sets the stage for more accurate and predictive modeling of these complex phenomena.

The established understanding of how systems reach thermal equilibrium is facing refinement as researchers increasingly explore the behavior of strongly interacting quantum systems. Conventional statistical mechanics relies on the equivalence between different ensembles, ways of averaging over all possible states, but this assumption doesn’t always hold, particularly when interactions are long-range. Consequently, predictions for observable properties derived from each ensemble will naturally diverge. The team developed a perturbative theory that provides analytical expressions for both the height of the prethermal plateau and its timescale, and uncovered a symmetry-imposed selection rule that restricts which system sizes can be compared within this fragmented eigenstate thermalization hypothesis (fETH). This band-resolved description has direct consequences for equilibrium statistical mechanics, as microcanonical ensembles remain confined to a single band while canonical ensembles mix different bands, explaining ensemble inequivalence without invoking equilibrium phase transitions. Our results apply to a broad class of Hamiltonians exhibiting Hilbert-space fragmentation.