Ergodic properties of a generic non-integrable quantum many-body system in thermodynamic limit

TL;DR

This paper investigates the ergodic and transport properties of a generic non-integrable quantum many-body system, revealing phase transitions between ballistic and diffusive regimes and proposing an order parameter for these transitions.

Contribution

It demonstrates the existence of a phase transition from non-ergodic to ergodic behavior in a non-integrable quantum system using multiple analytical and numerical methods.

Findings

Ballistic transport in integrable and intermediate regimes

Normal diffusive transport in strongly non-integrable regime

Exponential decay of time-correlation functions in ergodic phase

Abstract

We study a generic but simple non-integrable quantum {\em many-body} system of {\em locally} interacting particles, namely a kicked $t-V$ model of spinless fermions on 1-dim lattice (equivalent to a kicked Heisenberg XX-Z chain of 1/2 spins). Statistical properties of dynamics (quantum ergodicity and quantum mixing) and the nature of quantum transport in {\em thermodynamic limit} are considered as the kick parameters (which control the degree of non-integrability) are varied. We find and demonstrate {\em ballistic} transport and non-ergodic, non-mixing dynamics (implying infinite conductivity at all temperatures) in the {\em integrable} regime of zero or very small kick parameters, and more generally and important, also in {\em non-integrable} regime of {\em intermediate} values of kicked parameters, whereas only for sufficiently large kick parameters we recover quantum ergodicity and mixing implying normal (diffusive) transport. We propose an order parameter (charge stiffness $D$) which controls the phase transition from non-mixing/non-ergodic dynamics (ordered phase, $D>0$) to mixing/ergodic dynamics (disordered phase, D=0) in the thermodynamic limit. Furthermore, we find {\em exponential decay of time-correlation function} in the regime of mixing dynamics. The results are obtained consistently within three different numerical and analytical approaches: (i) time evolution of a finite system and direct computation of time correlation functions, (ii) full diagonalization of finite systems and statistical analysis of stationary data, and (iii) algebraic construction of quantum invariants of motion of an infinite system, in particular the time averaged observables.