Eigenstate thermalization in thermal first-order phase transitions

TL;DR

This paper explores how the eigenstate thermalization hypothesis (ETH) must be extended to account for thermal first-order phase transitions, revealing coexistence of distinct eigenstate classes and eigenstate phase transitions.

Contribution

The work introduces a class of all-to-all spin models with thermal first-order transitions, demonstrating the need to generalize ETH near such transitions and identifying eigenstate coexistence and superpositions.

Findings

Eigenstate expectation values can differ across phases at the same energy.

Coexistence of eigenstates associated with different mean-field solutions.

Identification of eigenstate phase transitions separating regimes.

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 requires 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 mean-field solutions (two ``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 Schrodinger-cat-like eigenstates that are inter-branch superpositions; these two regimes are separated by an eigenstate phase transition. We 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 non-equilibrium dynamics.