Dynamics and Thermalization in Many-Body Quantum Systems I

We study the onset of quantum chaos as integrable models with local conservation laws are perturbed. We show that chaos emerges immediately for arbitrarily small perturbations even in finite systems for the spin models we studied. This chaos takes place due to the uplifting of the degeneracies in each sector with a fixed value of the local conservation law present in the integrable model, as we show by analyzing some eigenstate thermalization hypothesis (ETH) indicators and the bipartite entanglement entropy. The system transitions to another chaotic regime as the perturbation strength grows as states from different sectors start to mix, resulting in a fully ergodic spectrum after this transition. The transition is signaled by a maximal sensitivity of the eigenstates to perturbation marked by developing peaks of the typical fidelity susceptibilities that move polynomially to vanishing perturbation strength in the thermodynamic limit. Additionally, we show that the low-frequency limit of the spectral function agree with expectation from the random matrix theory (RMT) for both the chaotic but not ergodic and the ergodic regimes, while it diverges around the transition. We conclude by showing that similar physics holds in 2D as well, by studying the transverse field Ising model.