Ergodicity and Entanglement: Bridging Random Matrix Theory and Many-Body Quantum Systems

Thermalization is deeply connected to the notion of ergodicity in the Hilbert space, implying an equipartition of the wave function over available many-body Fock states. Under unitary time evolution, an initially structured state spreads in the Fock space, approaching a Haar random state, thereby highlighting a connection between many-body quantum systems and random matrix theory.

In the first part of this talk, I will discuss the dynamics of the self-dual kicked Ising model, a minimal model of many-body quantum chaos that is unitary in both time and space. I will focus on its dynamics in Fock space, showing how the probability distribution of the initial state approaches that of a random state (Porter-Thomas distribution).

In the second part, I will explore some general relationships between entanglement and the spread of the wave function in Fock space. Remarkably, I will demonstrate that entanglement entropies can still exhibit fully ergodic behavior, even though the wave function occupies only a vanishing fraction of the full Hilbert space in the thermodynamic limit.