Random multipolar driving: tunably slow heating through spectral engineering

We study heating in interacting quantum many-body systems driven by random sequences with n−multipolar correlations, corresponding to a polynomially suppressed low frequency spectrum. For n ≥ 1, we find a prethermal regime, the lifetime of which grows algebraically with the driving rate, with exponent 2n + 1. A simple theory based on Fermi’s golden rule accounts for this behaviour. The quasiperiodic Thue-Morse sequence corresponds to the n →∞ limit, and accordingly exhibits an exponentially long-lived prethermal regime. Despite the absence of periodicity in the drive, and in spite of its eventual heat death, the prethermal regime can host versatile non-equilibrium phases, which we illustrate with a random multipolar discrete time crystal.