Out-of-time-ordered correlator in time evolution from a prepared initial state in many-body localization

Abstract

We investigate the time evolution of out-of-time-ordered correlator (OTOC) in a disordered spin-1/2 XXZ Heisenberg chain. We find that a choice of initial state strongly affects the distributions of OTOC across the random disorder realizations. The distributions of OTOC show two types in their shape: one is very spiky and the other spreads widely over a possible range of OTOC. We analyze the distributions by using the inverse participation ratio (IPR) which gets smaller as the eigenstates more evenly are superposed in the initial state. We find that the initial state having the spiky distribution of OTOC shows a small IPR while the other having the broad distribution of OTOC shows a large IPR. We argue that a preparation of a optimal initial state can be relevant for the measurement of OTOC in a time evolution experiment with trapped ion.