Confinement and Mott transitions of One-dimensional Z₂ Lattice Gauge Theories with Dynamical Matter

Confinement is an ubiquitous phenomenon when matter couples to gauge fields, which manifests itself in a linear string potential between two static charges. Although gauge fields can be integrated out in one dimension, they can mediate non-local interactions which in turn influence the paradigmatic Luttinger liquid properties. However, when the charges become dynamical and their densities finite, understanding confinement becomes challenging. In my talk I will show that confinement in 1D Z₂ lattice gauge theories, with dynamical matter fields and arbitrary densities, is related to translational symmetry breaking in a non-local basis. The exact transformation to this string-length basis leads us to an exact mapping of Luttinger parameters reminiscent of a Luther-Emery re-scaling.

In addition we include the effects of local, but beyond contact, interactions between the matter particles, and show that confined mesons can form a Mott-insulating state when the deconfined charges cannot. While the transition to the Mott state cannot be detected in the Green's function of the charges, we show that the metallic state is characterized by hidden off-diagonal quasi-long range order. In addition we find that the model exhibits remarkably different phase diagrams at different fillings. In particular we focused on the filling of two-third and one-half where we found signatures of super-solid behaviour. Our predictions provide new insights to the physics of confinement of dynamical charges, and can be experimentally addressed in Rydberg-dressed quantum gases in optical lattices.