Does a Single Eigenstate of a Hamiltonian Encode the Critical Behaviour of its Finite-Temperature Phase Transition?

TL;DR

This paper argues that a single energy eigenstate of a non-integrable quantum system can encode the critical behavior associated with its finite-temperature phase transition, supported by theoretical reasoning and numerical evidence.

Contribution

It introduces a theoretical framework and numerical validation showing that individual eigenstates contain information about the system's critical phenomena.

Findings

Eigenstates encode critical behavior of phase transitions

Theoretical argument supports eigenstate encoding of criticality

Numerical results confirm the presence of critical information in eigenstates

Abstract

Recent work on the subject of isolated quantum thermalization has suggested that an individual energy eigenstate of a non-integrable quantum system may encode a significant amount of information about that system's Hamiltonian. We provide a theoretical argument, along with supporting numerics, that this information includes the critical behaviour of a system with a second-order, finite-temperature phase transition.