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

by Stéphane Vinet, Gabriel Longpré, William Witczak-Krempa

Submission summary

As Contributors: Gabriel Longpre · Stéphane Vinet
Arxiv Link: https://arxiv.org/abs/2107.04615v2 (pdf)
Date submitted: 2021-08-10 17:54
Submitted by: Longpre, Gabriel
Submitted to: SciPost Physics Core
Academic field: Physics
Specialties:
  • Condensed Matter Physics - Theory
  • Quantum Physics

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.

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Submission 2107.04615v2 on 10 August 2021

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