Exploring Phase Diagrams of 1D Z₂ Lattice-Gauge Theory with Dynamical Matter

Here, we study a one-dimensional lattice-gauge theory model where dynamical charges are coupled to gauge fields. Such models exhibit confinement and can be realized with modern quantum simulators. By adding nearest-neighbor interactions we uncover interesting phase transitions to different Mott states, which are strongly related to the filling. Remarkably, the confining electric field stabilizes a Mott state at the filling of n = 2/3 and destabilizes it for filling n = 1/2. On the other hand, adding superconducting terms instead of the nearest-neighbor interactions results in trivial to non-trivial topological transitions, which resemble behavior of the Kitaev chain. In our work we rely on the combination of the numerical DMRG calculations and analytical techniques, which are tractable for specific parameter values and limits. We also develop an effective mean-field theory model of our problem. This simple mean-field model correctly resembles the main features of the original model and offers deeper physical insights. Finally, we also discuss possible experimental realizations with quantum gases in optical lattices.