Emergent statistical bubble localization in a Z_2 lattice gauge theory

摘要

We introduce a clean cluster spin chain coupled to fully interacting spinless fermions, forming an unconstrained Z(2) lattice gauge theory (LGT), which possesses dynamical proximity effect controlled by the entanglement structure of the initial state. We expand the machinery of interaction-driven localization to the realm of LGTs such that for any starting product state, the matter fields exhibit emergent statistical bubble localization, which is driven solely by the cluster interaction, having no topologically trivial noninteracting counterpart, and thus is of a pure dynamical many-body effect. In this vein, our proposed setting provides possibly the minimal model dropping all the conventional assumptions regarding the existence of many-body localization. Through projective measurement of local constituting species, we also identify the coexistence of the disentangled nonergodic matter and thermalized gauge degrees of freedom, which stands completely beyond the standard established phenomenology of quantum disentangled liquids. As a byproduct of self-localization of the proximate fermions, the spin subsystem hosts the long-lived topological edge zero modes, which are dynamically decoupled from the thermalized background Z(2) charges of the bulk, and hence remains cold at arbitrary high-energy density. This provides a convenient platform for strong protection of the quantum bits of information, which are embedded at the edges of completely ergodic subsystem; the phenomenon that in the absence of such proximity-induced self-localization could, at best, come about with a prethermal manner in translational invariant systems. Finally, by breaking local Z(2) symmetry of the model, we argue that such admixture of particles no longer remains disentangled and the ergodic gauge degrees of freedom act as a "small bath" coupled to the localized components.