Universality of Dynamical Localization in Periodically Driven Spin Systems: From Simple Quantum Magnets to Disordered and Long-Range Models

Dynamical localization is one of the most startling manifestations of quantum interference, where the expected infinite temperature thermalization of a periodically driven quantum system is prevented by infinite hysteresis. The basic idea is that a driven system gets frozen when its instantaneous relaxation rate falls below the driving rate. The system is said to be "Dynamically Localized" at that state. Freezing can be seen as a many body generalization of Coherent Destruction of Tunneling (CDT), where single particle quantum systems can be localized in space as the ratio of the drive frequency and amplitude tends to certain specific values (the freezing condition).

We demonstrate the onset of freezing in periodically driven Ising spins with nearest neighbour interactions[1]. We then explore the universality of this phenomenon by investigating the fate of freezing in quantum many body systems with lower symmetries. These include the Ising model with disorder[2], as well as long range interactions. In the former case, we demonstrate that, although random interactions kill freezing eventually, spectacular remnants survive even with strong disorder. Finally, we summarize ongoing explorations of the fate of freezing in long-range spin systems. We present analysis and numerics for the periodically driven Lipkin-Meshkov-Glick (LMG) model [3,4]. In this system, the same dynamical localization appears in the thermodynamic limit, as well for finite sized systems. In addition, we discuss ongoing numerical studies of localization when the spins have power-law interactions. We expect that approximate simulations of the quantum phase space dynamics, together with the addition of quantum correlations due to the BBGKY evolution, will bring about highly accurate estimates of the correlations, demonstrating the persistence of freezing in these systems.