Variational Wave-Function Analysis of the Fractional Anomalous Hall Crystal

Abstract

We propose fractional anomalous Hall crystals (FAHCs) as possible ground states of strongly interacting electrons in parent bands with Berry curvature. FAHCs are exotic states of matter that spontaneously break continuous translation symmetry to form a fractional Chern insulator. We construct a unified family of variational wave functions that describe FAHCs and their competing states in the presence of uniform parent Berry curvature. We calculate their variational energy with Coulomb interactions semianalytically in the thermodynamic limit. Our analysis reveals that FAHCs can be energetically favorable over both Wigner crystals and integer anomalous Hall crystals for sufficiently strong interactions or flat dispersion.