Two-dimensional Ising gauge theory coupled to single-component fermion matter: topological order, confinement and fractons
I will present our investigations of the rich quantum phase diagram of Wegner's theory of discrete Ising gauge fields interacting with U(1) symmetric single-component fermion matter hopping on a two-dimensional square lattice. In particular limits the model reduces to (i) pure Z_2 even and odd gauge theories, (ii) free fermions in a static background of deconfined Z_2 gauge fields, (iii) the kinetic Rokhsar-Kivelson quantum dimer model at a generic dimer filling. I will introduce a local transformation that maps the lattice gauge theory onto a model of Z_2 gauge-invariant spin 1/2 degrees of freedom and will discuss its merits. In the absence of the magnetic plaquette term, I will present evidence of topologically ordered Dirac semimetal and staggered Mott insulator phases at half filling. I will present our investigations of the nature of the exotic phase transition between these phases. At strong coupling, the lattice gauge theory displays emergent fracton phenomenology with isolated fermions being completely frozen and dimers exhibiting restricted mobility. In that limit, I will argue that in the ground state dimers form compact clusters, whose hopping is suppressed exponentially in their size.