Correlation and entanglement dynamics of free fermions in disguise

Abstract

We study the nonequilibrium dynamics following a quantum quench in spin chains that can be solved via a mapping to free fermions in disguise. These models feature an exponential degeneracy of all energy eigenvalues, raising the question of the validity of the established framework describing the properties of integrable systems out of equilibrium. We present two main results. First, we develop an analytic method to compute the quasi-momentum distribution function characterizing the generalized Gibbs ensemble, and derive an analytic formula to compute the corresponding expectation values for special observables. Second, we adapt the standard formula for the entanglement growth based on the quasi-particle picture, discussing how our constructions do not explicitly make use of the zero-energy auxiliary free fermions responsible of the exponential degeneracies. We test our theoretical predictions against numerical tensor-network computations for different initial states and Hamiltonian parameters. For the local observables, we find excellent agreement. For the entanglement dynamics, we find small deviations suggesting that the standard quasi-particle picture is only approximately correct for the initial state considered. Our results represent a first step towards the extension of the established framework of integrable systems out of equilibrium to models hosting free fermions in disguise.