Time evolution of a quantum many-body system: transition from integrability to ergodicity in thermodynamic limit

TL;DR

This paper investigates the transition from non-ergodic to ergodic behavior in a quantum many-body system, showing how transport properties change with system parameters and linking these to integrability and random matrix theory.

Contribution

It provides numerical evidence of a transition from non-ergodic to ergodic behavior in a non-integrable quantum system as parameters increase, connecting transport phenomena to underlying dynamics.

Findings

Non-ergodic behavior with ideal transport observed in certain parameter regimes.

Transition to ergodicity and normal transport occurs at large kick parameters.

Quantum ergodicity aligns with predictions from random matrix theory.

Abstract

Numerical evidence is given for non-ergodic (non-mixing) behavior, exhibiting ideal transport, of a simple non-integrable many-body quantum system in the thermodynamic limit, namely kicked $t-V$ model of spinless fermions on a ring. However, for sufficiently large kick parameters $t$ and $V$ we recover quantum ergodicity, and normal transport, which can be described by random matrix theory.