Exact Thermal Eigenstates of Nonintegrable Spin Chains at Infinite Temperature

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.

6 pages, 2 figures and Supplemental Material

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• Exact volume-law entangled zero-energy eigenstates in a large class of spin models
• Proof of absence of local conserved quantities in two- and higher-dimensional quantum Ising models
• Numerical extraction of crosscap coefficients in microscopic models for (2+1)D conformal field theory
• Dichotomy theorem separating complete integrability and non-integrability of isotropic spin chains
• Symmetric tensor scars with tunable entanglement from volume to area law
• Spatially Structured Entanglement from Nonequilibrium Thermal Pure States
• Stable infinite-temperature eigenstates in SU(2)-symmetric nonintegrable models
• No boundary density matrix in elliptic de Sitter dS/${\mathbb{Z}}_2$
• Exact Quench Dynamics from Thermal Pure Quantum States
• Additional quantum many-body scars of the spin-$1$ $XY$ model with Fock-space cages and commutant algebras