Role of energy uncertainties in ergodicity breaking induced by competing interactions and disorder. A dynamical assessment through the Loschmidt echo

TL;DR

This paper investigates how energy uncertainties from disorder and interactions influence ergodicity breaking in quantum many-particle systems, using the Loschmidt echo as a dynamical probe to identify phase transitions and critical thresholds.

Contribution

It introduces a dynamical assessment method using the Loschmidt echo to map ergodic and non-ergodic phases and estimates critical lines considering energy uncertainties.

Findings

Loschmidt echo effectively distinguishes ergodic and non-ergodic phases.

Energy uncertainties shift phase transition thresholds.

Critical lines align with phase diagram from LE dynamics.

Abstract

A local excitation in a quantum many-particle system evolves deterministically. A time-reversal procedure, involving the invertion of the signs of every energy and interaction, should produce an excitation revival: the Loschmidt echo (LE). If somewhat imperfect, only a fraction of the excitation will refocus. We use such a procedure to show how non-inverted weak disorder and interactions, when assisted by the natural reversible dynamics, fully degrade the LE. These perturbations enhance diffusion and evenly distribute the excitation throughout the system. Such a dynamical paradigm, called ergodicity, breaks down when either the disorder or the interactions are too strong. These extreme regimes give rise to the well known Anderson localization and Mott insulating phases, where quantum diffusion becomes restricted. Accordingly, regardless of the kinetic energy terms, the excitation remains mainly localized and out-of-equilibrium, and the system behaves non-ergodically. The LE constitutes a fair dynamical witness for the whole phase diagram since it evidences a surprising topography in which ergodic and non-ergodic phases interpenetrate each other. Furthermore, we provide an estimation for the critical lines separating the ergodic and non-ergodic phases around the Mott and Anderson transitions. The energy uncertainties introduced by disorder and interaction shift these thresholds towards stronger perturbations. Remarkably, the estimations of the critical lines are in good agreement with the phase diagram derived from the LE dynamics.