Exact Thermal Eigenstates of Nonintegrable Spin Chains at Infinite Temperature

TL;DR

This paper analytically constructs thermal eigenstates of nonintegrable spin chains at infinite temperature, providing a potential proof of the eigenstate thermalization hypothesis (ETH) in realistic quantum systems.

Contribution

It introduces entangled antipodal pair (EAP) states as analytically tractable thermal eigenstates and identifies nonintegrable Hamiltonians with these states as eigenstates.

Findings

EAP states are indistinguishable from Gibbs states at infinite temperature.

Certain Hamiltonians with EAP eigenstates are proven to be nonintegrable.

A thermal pure state at arbitrary temperature can be generated from EAP states via imaginary time evolution.

Abstract

The eigenstate thermalization hypothesis (ETH) plays a major role in explaining thermalization of isolated quantum many-body systems. However, there has been no proof of the ETH in realistic systems due to the difficulty in the theoretical treatment of thermal energy eigenstates of nonintegrable systems. Here, we write down analytically thermal eigenstates of nonintegrable spin chains. We consider a class of theoretically tractable volume-law states, which we call entangled antipodal pair (EAP) states. These states are thermal, in the most fundamental sense that they are indistinguishable from the Gibbs state with respect to all local observables, with infinite temperature. We then identify Hamiltonians having the EAP state as an eigenstate and rigorously show that some of these Hamiltonians are nonintegrable. Furthermore, a thermal pure state at an arbitrary temperature is obtained by the imaginary time evolution of an EAP state. Our results offer a potential avenue for providing a provable example of the ETH.