Random multipolar driving: tunably slow heating through spectral engineering

Driven quantum systems may realize novel phenomena absent in static systems, but driving-induced heating can limit the time-scale on which these persist. 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 ngeq1, 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→ infty 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.