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Localization Dynamics and Gauge Theories from Mobile Quantum Impurities

We study the interplay between superfluid Meissner response, localization dynamics from impurities and gauge theories. The superfluidity is formed in the rung-Mott phase of the bosonic ladder model producing spin-Meissner currents induced by a U(1) gauge field or a uniform magnetic field. Impurities are described through two-state systems which act as a two-peak random potential. An impurity sits either at the top or at the bottom of the ladder on each rung equally, producing a telegraph signal. The impurities-matter coupling gives rise to an intrinsic Z2 gauge theory. Through analytical approaches and numerical exact diagonalization, we address both the weakly-coupled and strongly-coupled rungs limits for impurities. In the weakly-coupled rungs situation, we find a smooth power-law localization whereas the strongly-coupled rungs limit produces a steep localization or insulating phase for various configurations of the potential. We describe the superfluid response relying on quantum spin models showing four-particles coupling in the strongly-interacting regime with impurities and linking with the persistent current limit. Through entanglement and bipartite fluctuation measures, we also identify a many-body localization regime in time after a quench of the system when prepared in a Néel state.