Abstract

Isolated quantum dynamics need not lead to local thermal equilibrium in the presence of sufficient quenched disorder. This many-body localized phase is not described by equilibrium statistical mechanics. At lower disorder however, the system transitions into a conventional thermal phase. Very little is known about the dynamical transition between the two phases, especially in spatial dimensions greater than one. In this talk, I will introduce a simple circuit model for the localization-delocalization dynamical transition in the absence of global symmetries. The tractability of the model arises from the restriction of the gates in the circuit to Clifford gates. In d=1, the resulting dynamics are always many-body localized with a complete set of strictly local integrals of motion. In d>=2, the system realizes both localized and delocalized phases separated by a continuous transition in which ergodic puddles percolate. I will argue that the phases are stable to small deformations of the circuits, estimate the resulting phase boundary and conjecture bounds on the critical exponents for the generic transition. The Clifford circuit model is a distinct tractable limit from that of free fermions and is a toy dynamical system to test thermalization in.