Aleksander Avdoshkin: Eigenstate thermalization in thermal first-order phase transitions

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, I will discuss (based on our recent preprint arXiv:2601.08347) how it requires generalization in the presence of thermal first-order phase transitions (1OPT). I will introduce a class of all-to-all spin models, featuring 1OPT that stem from two distinct mean-field solutions that exchange dominance in the many-body density of states as the energy is varied. We argued for a part of the energy spectrum, 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 at the same energy density, and another regime with Schrodinger-cat-like eigenstates that are inter-branch superpositions. The results are supported by a semiclassical calculations and an exact diagonalization study of a microscopic spin model. I will also cover how our works connects to broader (not yet understood) questions concerning dynamics of 1OPT and many-body metastability at the quantum level.