Quantum chaos and thermalization in random quantum circuits

The question of how statistical mechanics behavior emerges from the unitary dynamics of isolated quantum interacting systems can be well understood using an assumption about the structure of the energy eigenstates, known as the eigenstate thermalization hypothesis (ETH). ETH is a natural extension of the random matrix theory (RMT) and establishes a connection between quantum thermalization and the notion of quantum chaos. In this talk, I will present our analytical studies on quantum chaos and eigenstate thermalization in a large family of random quantum circuits. A field theoretical approach is used to investigate the statistical properties of quasienergy eigenstates and eigenvalues, and this method can be generalized to explore other fundamental features of various quantum circuit models. Our calculation of energy level correlation function shows that all the random quantum circuits under consideration exhibit the universal RMT level statistics, a defining property of quantum chaos. Our analysis of eigenstate correlation function provides analytical support for ETH and also suggests that the spectral form factor, a measure of level statistics, determines the time dependence of the approach to thermal equilibrium.