Symmetries and Fractionalization in Fractional Chern Insulators via a Composite Fermion Theory

Fractional Chern Insulators (FCIs) are two dimensional interacting lattice systems which realize analogues of the Fractional Quantum Hall Effect (FQHE). Like FQH states, FCIs possess anyonic excitations and so can exhibit symmetry fractionalization, a phenomenon in which the anyons transform projectively under the symmetries of the system. For instance, fractionalization of the U(1) symmetry of FQH states and FCIs leads to the anyons carrying fractional charge. FCIs also possess additional lattice symmetries; in particular, the lattice translational symmetry may be fractionalized resulting in anyons carrying fractional momenta. Previously, we developed a composite fermion theory of FCIs on a Kagome lattice model (wherein fermions are mapped to composite fermions coupled to a lattice Chern-Simons gauge field). We illustrate how, using this approach, a Kagome lattice model can support FCIs realizing a large range of translational symmetry fractionalization classes. Our formalism also opens the possibility of investigating the competition and coexistence of FCIs with symmetry-broken states.