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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- 1 Université de Montréal / University of Montreal
- 2 Regroupement Québécois sur les Matériaux de Pointe [RQMP]
- Fonds Québécois de la Recherche sur la Nature et les Technologies (through Organization: Fonds de Recherche du Québec – Nature et technologies [FRQNT])
- Conseil de Recherches en Sciences Naturelles et en Génie / Natural Sciences and Engineering Research Council [NSERC / CRSNG]