Effective model for a quantum Hall crystal

A Hall crystal is a phase of matter with spontaneously broken translation symmetry and a quantized Hall conductance. We present a two-dimensional lattice model whose ground-state realizes a quantum Hall crystal. We employ the Chern-Simons Ginzburg Landau theory (CSGL) in which the quantum Hall state is a condensate of bosons bound to an odd number of flux quanta. In this description, a Hall crystal is a supersolid phase of these bosons. We present the phase diagram of this system, which consists of superfluid, supersolid, and Wigner crystalline phases of bosons. These correspond respectively to the quantum Hall liquid, Hall crystal, and Wigner crystalline phases of electrons.