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 locally interacting particles, namely, a kicked-parameter $\mathrm{}(t,V)\mathrm{}$ model of spinless fermions on a one-dimensional lattice (equivalent to a kicked Heisenberg $\mathrm{XX}-Z$ chain of $1/2$ spins). The statistical properties of the dynamics (quantum ergodicity and quantum mixing) and the nature of quantum transport in the thermodynamic limit are considered as the kick parameters (which control the degree of nonintegrability) are varied. We find and demonstrate ballistic transport and nonergodic, nonmixing dynamics (implying infinite conductivity at all temperatures) in the integrable regime of zero or very small kick parameters, and more generally and importantly, also in the nonintegrable regime of intermediate values of kicked parameters, whereas only for sufficiently large kick parameters do we recover quantum ergodicity and mixing implying normal (diffusive) transport. We propose an order parameter (charge stiffness $D)$ which controls the phase transition from nonmixing and nonergodic dynamics (ordered phase, $D>\mathrm{}0)$ to mixing and ergodic dynamics (disordered phase, $D=0)$ in the thermodynamic limit. Furthermore, we find exponential decay of time correlation functions 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.