Ergodic properties of a generic nonintegrable quantum many-body system in the thermodynamic limit

We study a generic but simple nonintegrable quantum many-body system of loc ally interacting particles, namely, a kicked-parameter (t,V) model of spinl ess fermions On a one-dimensional lattice (equivalent to a kicked Heisenber g XX-Z chain of 1/2 spins). The statistical properties: of the dynamics (qu antum ergodicity and quantum mixing) and the nature of quantum transport in the thermodynamic limit are considered as the kick parameters (which contr ol the degree of nonintegrability) are varied. We find and demonstrate ball istic transport and nonergodic, nonmixing dynamics (implying infinite condu ctivity at all temperatures) in the integrable regime of zero or very small kick parameters, and more:generally and importantly, also in the nonintegr able regime of intermediate values of kicked parameters, whereas only for s ufficiently large kick parameters do we recover quantum ergodicity and mixi ng implying normal (diffusive) transport. We propose an order parameter (ch arge stiffness D) which controls the phase transition from nonmixing and no nergodic dynamics (ordered phase, D > 0) to mixing and ergodic dynamics (di sordered phase, D = 0) in the thermodynamic limit. Furthermore, we find exp onential decay of rime correlation functions in the regime of mixing dynami cs. 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 fi nite systems and statistical analysis of stationary data, and (iii) algebra ic construction of quantum invariants of motion of an infinite system, in p articular the time-averaged observables. [S1063-651X(99)10710-3].