Interaction-disorder competition in a spin system evaluated through the Loschmidt echo

The interplay between interactions and disorder in closed quantum many-body systems is relevant for thermalization phenomenon. In this paper, we address this competition in an infinite temperature spin system by means of the Loschmidt echo (LE), which is based on a time reversal procedure. This quantity has been formerly employed to connect quantum and classical chaos, and in the present many-body scenario we use it as a dynamical witness. We assess the LE time scales as a function of disorder and interaction strengths. The strategy enables a qualitative phase diagram that shows the regions of ergodic and nonergodic behavior of the polarization under the echo dynamics.Instituto de Física La Plat