Excitations and ergodicity of critical quantum spin chains from non-equilibrium classical dynamics

TL;DR

This paper explores the excitations and ergodic behavior of a quantum spin chain dual to classical non-equilibrium dynamics, revealing complex excitation spectra and non-integrability indicative of ergodicity.

Contribution

It introduces an exact ground state solution for a disordered quantum Ising-Kawasaki chain and analyzes its excitation spectrum and ergodic properties.

Findings

Two-magnon solutions derived via Bethe Ansatz.

Presence of multiple dynamical critical exponents.

System is non-integrable and ergodic for generic parameters.

Abstract

We study a quantum spin-1/2 chain that is dual to the canonical problem of non-equilibrium Kawasaki dynamics of a classical Ising chain coupled to a thermal bath. The Hamiltonian is obtained for the general disordered case with non-uniform Ising couplings. The quantum spin chain (dubbed Ising-Kawasaki) is stoquastic, and depends on the Ising couplings normalized by the bath's temperature. We give its exact ground states. Proceeding with uniform couplings, we study the one- and two-magnon excitations. Solutions for the latter are derived via a Bethe Ansatz scheme. In the antiferromagnetic regime, the two-magnon branch states show intricate behavior, especially regarding their hybridization with the continuum. We find that that the gapless chain hosts multiple dynamics at low energy as seen through the presence of multiple dynamical critical exponents. Finally, we analyze the full energy level spacing distribution as a function of the Ising coupling. We conclude that the system is non-integrable for generic parameters, or equivalently, that the corresponding non-equilibrium classical dynamics are ergodic.