Critical quantum spin chains from non-equilibrium classical dynamics: level statistics and entanglement entropy

A critical quantum spin 1/2 chain dual to the non-equilibrium Kawasaki dynamics of an Ising chain coupled to a bath is presented. Its level spacing distributions are analysed in the context of random matrix theory. The implications on the integrability of the system are discussed. Scaling of the entanglement entropy of exact states is studied against the eigenstate thermalization hypothesis.