Arrested operator spreading in a family of random two-layer Floquet Clifford circuits in one dimension

Abstract

Many-body localization has been popularly characterized as the absence of thermalization in disordered interacting quantum systems in which an emergent set of exponentially localized operators is believed to explain many aspects of phenomenology of disordered many-body systems, which includes the tendency to retain memories of initial conditions and the logarithmically slow growth of entanglement entropy. This picture of operators and information spreading makes MBL attractive to study from the perspective of quantum circuits and quantum information theory. In this work, we revisit a family of random two-layer Floquet circuits composed of a restricted ensemble of two Clifford gates that can be tuned to exhibit ergodic and nonergodic dynamics. We observe the narrowing of the lightcone and the emergence of exponentially decaying behavior in the averaged out-of-time order correlator and total endpoint density, which display increasingly localized behavior in the nonergodic regime.