Numerical evidence is given for nonergodic (nonmixing) behavior, exhibiting ideal transport, of a simple nonintegrable many-body quantum system in the thermodynamic limit, namely, the 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.
Numerical evidence is given for nonergodic (nonmixing) behavior, exhibiting ideal transport, of a simple nonintegrable many-body quantum system in the thermodynamic limit, namely, the 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.
We study a generic but simple nonintegrable quantum many-body system of locally interacting particles, namely, a kicked-parameter (t,V) model of spinless fermions on a one-dimensional lattice (equivalent to a kicked Heisenberg 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>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.
A dynamical Lie algebraic method for the construction of quantum invariants of motion in non-integrable many-body systems of infinite size is proposed and applied to a simple but generic toy model, namely an infinite kicked t - V chain of interacting spinless fermions. The transition from an integrable via quasi-integrable ( intermediate ) to a quantum ergodic (quantum mixing) regime in parameter space is investigated. A dynamical phase transition between an ergodic and intermediate (neither ergodic nor completely integrable) regime in thermodynamic limit is proposed. The existence or non-existence of local conservation laws corresponds to the intermediate or ergodic regime, respectively. The computation of time-correlation functions of typical observables by means of local conservation laws is found to be fully consistent with direct calculations on finite systems.
In recent years, there has been growing interest in characterizing the complexity of quantum evolutions of interacting many-body systems. When a time-independent Hamiltonian governs the dynamics, Krylov complexity has emerged as a powerful tool. For unitary evolutions like kicked systems or Trotterized dynamics, a similar formulation based on the Arnoldi approach has been proposed yielding a new notion of quantum ergodicity [P. Suchsland, R. Moessner, and P. W. Claeys, Phys. Rev. B 111, 014309 (2025)10.1103/PhysRevB.111.014309]. In this work, we show that this formulation is robust for observing the transition from integrability to chaos in both autonomous and kicked systems. Examples from random matrix theory and spin chains are shown in this paper.
It is of great current interest to establish toy models of ergodicity breaking transitions in quantum many-body systems. Here, we study a model that is expected to exhibit an ergodic to nonergodic transition in the thermodynamic limit upon tuning the coupling between an ergodic quantum dot and distant particles with spin-1/2. The model is effectively zero dimensional; however, a variant of the model was proposed by De Roeck and Huveneers to describe the avalanche mechanism of ergodicity breaking transition in one-dimensional disordered spin chains. We show that exact numerical results based on the spectral form factor calculation accurately agree with theoretical predictions, and hence unambiguously confirm existence of the ergodicity breaking transition in this model. We benchmark specific properties that represent hallmarks of the ergodicity breaking transition in finite systems.
We analytically study the time evolution of the expectation values of observables in periodically kicked many-body quantum systems. Starting from an initial state, we compute both the transient and the long-time properties of the observables. Our derivation explains the criteria and the mechanism that lead to the infinite-temperature statistical average of observables at long times, irrespective of the initial state. When the criteria are violated, the observables oscillate with time. These oscillations are subharmonic and robust to small perturbations, suggesting the emergence of a discrete time crystal phase. We demonstrate these features explicitly in periodically kicked nonintegrable spin chains. For a spin chain with two kicks per cycle, we show that the kicked chain can exhibit an ergodic or a discrete-time crystal phase for the same kicking strengths, depending on the initial state preparation. We complement our time-evolution study of observables with the spectral form factor of these kicked models.