Fock-space delocalization and the emergence of the Porter-Thomas distribution from dual-unitary dynamics

The chaotic dynamics of quantum many-body systems are expected to quickly randomize any structured initial state, delocalizing it in Fock space. In this work, we study the spreading of an initial product state in Hilbert space under dual-unitary dynamics, captured by the inverse participation ratios and the distribution of overlaps (bit-string probabilities). We consider the self-dual kicked Ising model, a minimal model of many-body quantum chaos which can be seen as either a periodically driven Floquet model or a dual-unitary quantum circuit. Both analytically and numerically, we show that the inverse participation ratios rapidly approach their ergodic values, corresponding to those of Haar random states, and establish the emergence of the Porter-Thomas distribution for the overlap distribution. Importantly, this convergence happens exponentially fast in time, with a time scale that is independent of system size. We inspect the effect of local perturbations that break dual-unitarity and show a slowdown of the spreading in Fock space, indicating that dual-unitary circuits are maximally efficient at preparing random states.