Exact Thermal Eigenstates of Nonintegrable Spin Chains at Infinite Temperature

The eigenstate thermalization hypothesis (ETH) plays a major role inexplaining thermalization of isolated quantum many-body systems. However, therehas been no proof of the ETH in realistic systems due to the difficulty in thetheoretical treatment of thermal energy eigenstates of nonintegrable systems.Here, we write down analytically thermal eigenstates of nonintegrable spinchains. We consider a class of theoretically tractable volume-law states, whichwe call entangled antipodal pair (EAP) states. These states are thermal, in themost fundamental sense that they are indistinguishable from the Gibbs statewith respect to all local observables, with infinite temperature. We thenidentify Hamiltonians having the EAP state as an eigenstate and rigorously showthat some of these Hamiltonians are nonintegrable. Furthermore, a thermal purestate at an arbitrary temperature is obtained by the imaginary time evolutionof an EAP state. Our results offer a potential avenue for providing a provableexample of the ETH.

Further reading#

• Access Paper in arXiv.org