Emergence of self-averaging in non-unitary quench dynamics of chaotic many-body quantum systems

In typical isolated many-body quantum systems, the interplay of interaction and disorder leads to chaos, characterized by correlated eigenvalues and ergodic eigenstates. These features get manifested in the dynamics of the survival probability (overlap of the initial and the time-evolved state) and the spin autocorrelation function in the form of the dip-ramp-plateau structure, also known as the correlation hole. However, the onset of this structure requires large ensemble averages due to the lack of self-averaging of those quantities, i.e. the relative variance of their ensemble averaged value does not decay upon increasing system size. In this presentation, we show that by breaking the unitarity of the time evolution, we induce self-averaging. This is achieved by opening the system and allowing for energy dephasing. We consider three experimental systems to demonstrate the emergence of self-averaging: the one-dimensional disordered Heisenberg chain, the disordered Ising Hamiltonian with long-range interactions, and the non-interacting Anderson model.