Z₂Lattice Gauge System and Dynamical Localization

Gauge theory has been playing a fundamental role in our understanding of the deepest mysteries of physics. And recent advances in cold atom physics have also made the study of dynamical gauge systems a new frontier. Using Floquet approach, we propose to realize a one-dimensional Z₂ lattice gauge model, featuring extensive local constants of motions, using two specifies of Rb atoms. The resulting Floquet Hamiltonian turns out to be quite simple. Within a given symmetry sector of good quantum numbers, the system can be viewed as a 1D transverse quantum Ising model with a binary random longitudinal field. Therefore, the dynamics of the system is essentially controlled by disordered Hamiltonians, implying that the system can feature many body localization (MBL) as a result of dynamical localization. Numerical studies of energy level statistics and quench dynamics clearly demonstrate the existence of MBL phase in this system.