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

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.

9 pages, 1 figures

References in corpus (14)

• Thermalization and its mechanism for generic isolated quantum systems
• Localization of interacting fermions at high temperature
• Many body localization in Heisenberg XXZ magnet in a random field
• Ergodicity breaking in a model showing many-body localization
• Proof of the Ergodic Theorem and the H-Theorem in Quantum Mechanics
• Loschmidt Echo
• Long-Time Behavior of Macroscopic Quantum Systems: Commentary Accompanying the English Translation of John von Neumann's 1929 Article on the Quantum Ergodic Theorem
• Decoherence, Entanglement and Irreversibility in Quantum Dynamical Systems with Few Degrees of Freedom
• Experimental observation of a phase transition in the evolution of many-body systems with dipolar interactions
• Direct observation of quantum criticality in Ising spin chains
• NMR quantum simulation of localization effects induced by decoherence
• Effective one-body dynamics in multiple-quantum NMR experiments
• Quantum parallelism as a tool for ensemble spin dynamics calculations
• Decoherent time-dependent transport beyond the Landauer-Büttiker formulation: a quantum-drift alternative to quantum jumps

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