Interaction-induced transition in the quantum chaotic dynamics of a disordered metal

TL;DR

This paper investigates a transition in quantum chaotic behavior in disordered metals with interactions, showing how increasing temperature or interaction strength suppresses exponential growth in out-of-time-ordered correlators, indicating a shift from chaotic to non-chaotic dynamics.

Contribution

It reveals a temperature- and interaction-driven transition in quantum chaos in disordered metals, linking it to changes in energy-level statistics and proposing experimental observation methods.

Findings

Exponential growth of OTOC observed at weak interactions

Transition to non-chaotic behavior with increased temperature or interactions

Lyapunov exponent remains temperature-independent at weak interactions

Abstract

We demonstrate that a weakly disordered metal with short-range interactions exhibits a transition in the quantum chaotic dynamics when changing the temperature or the interaction strength. For weak interactions, the system displays exponential growth of the out-of-time-ordered correlator (OTOC) of the current operator. The Lyapunov exponent of this growth is temperature-independent in the limit of vanishing interaction. With increasing the temperature or the interaction strength, the system undergoes a transition to a non-chaotic behaviour, for which the exponential growth of the OTOC is absent. We conjecture that the transition manifests itself in the quasiparticle energy-level statistics and also discuss ways of its explicit observation in cold-atom setups.