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  • Open Access

Eigenstate Thermalization in Thermal First-Order Phase Transitions

Maksym Serbyn1,*, Alexander Avdoshkin2,*, Oriana K. Diessel3,4, and David A. Huse5

  • *These authors contributed equally to this work.
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Phys. Rev. X 16, 031042 – Published 18 August, 2026

DOI: https://doi.org/10.1103/4zs8-7kf4

Abstract

The eigenstate thermalization hypothesis (ETH) posits how isolated quantum many-body systems thermalize, assuming that individual eigenstates at the same energy density have identical expectation values of local observables in the limit of large systems. While the ETH apparently holds across a wide range of interacting quantum systems, in this work, we show that it may require generalization in the presence of thermal first-order phase transitions. We introduce a class of all-to-all spin models, featuring first-order thermal phase transitions that stem from two distinct local maxima of entropy (two mean-field solutions that we dub “branches”) that exchange dominance in the many-body density of states as the energy is varied. We argue that, for energies in the vicinity of the thermal phase transition, eigenstate expectation values do not need to converge to the same thermal value. The system has a regime with coexistence of two classes of eigenstates corresponding to the two branches with distinct expectation values at the same energy density and another regime with Schrödinger-cat-like eigenstates that are interbranch superpositions; these two regimes are separated by an eigenstate phase transition. We propose a more general form of the ETH Ansatz, support our results by semiclassical calculations and an exact diagonalization study of a microscopic spin model, and argue that the structure of eigenstates in the vicinity of thermal first-order phase transitions can be experimentally probed via nonequilibrium dynamics.

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Popular Summary

How does an isolated quantum system, undisturbed by any outside environment, reach thermal equilibrium on its own? The standard explanation, called the eigenstate thermalization hypothesis, assumes that every quantum eigenstate looks like the thermal state with the same energy. We show that this assumption breaks down when the system undergoes a thermal first-order phase transition—the abrupt kind of change seen when water boils. Using a model of many interacting spins, we find, as supported by analytical calculations and numerical simulations, that quantum eigenstates near the transition split into two families with sharply different properties, or merge into Schrödinger-cat states that are macroscopic superpositions of both phases at once. We propose a generalized hypothesis that captures both behaviors, and suggest signatures of such eigenstates in dynamics. Because such phase transitions are common, our results suggest that many quantum systems available in modern quantum simulators may realize this behavior.

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Outline

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Phys. Rev. X 16, 031042– Published 18 August, 2026
  • Received 27 January 2026
  • Revised 11 May 2026
  • Accepted 9 July 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

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