The fate of dynamical many-body localization in the presence of disorder

Abstract

Dynamical localization is one of the most startling manifestations of quantum interference, where the evolution of a simple system is frozen out under a suitably tuned coherent periodic drive. Here, we show that, although any randomness in the interactions of a many body system kills dynamical localization eventually, spectacular remnants survive even when the disorder is strong. We consider a disordered quantum Ising chain where the transverse magnetization relaxes exponentially with time with a decay time-scale $\tau$ due to random longitudinal interactions between the spins. We show that, under external periodic drive, this relaxation slows down ($\tau$ shoots up) by orders of magnitude as the ratio of the drive frequency $\omega$ and amplitude $h_0$ tends to certain specific values (the freezing condition). If $\omega$ is increased while maintaining the ratio $h_0/\omega$ at a fixed freezing value, then $\tau$ diverges exponentially with $\omega .$ The results can be easily extended for a larger family of disordered fermionic and bosonic systems.

Accepted for publication in Physical Review B Rapid Communications

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• Dynamical localization and slow dynamics in quasiperiodically-driven quantum systems
• Flow Equations for Disordered Floquet Systems
• Periodically and aperiodically Thue-Morse driven long-range systems: from dynamical localization to slow dynamics
• Phase Crossover induced by Dynamical Many Body Localization in Periodically Driven Long-Range Spin Systems
• Dynamical freezing and switching in periodically driven bilayer graphene
• Stretched-Exponential Melting of a Dynamically Frozen State Under Imprinted Phase Noise in the Ising Chain in a Transverse Field
• Strong frequency dependence of transport in the driven Fano-Anderson model
• Discrete time crystals in the presence of non-Markovian dynamics