Flux quantization for semions on a torus

Small systems of particles which obey fractional statistics with statistics parameter α=1/2, i.e., semions, on a lattice are studied by numerical diagonalization. The change in ground-state energy due to flux enclosure is calculated for various sizes of square lattices with periodic boundary conditions. Partial use is made of the translational symmetry properties of anyons on lattices with toroidal geometry. Using finite-size scaling, it is argued that the system exhibits true flux quantization, a signature of superfluidity, at rational fillings of the lattice less than 1/2. In agreement with previous work, no evidence of superfluidity is observed at lattice filling ν=1/2. However, in contrast to previous numerical studies, the results for ν>1/2 are noticeably different than those for ν<1/2. In particular, the signature of flux quantization generally is weaker for ν>1/2 and, in fact, is absent for some densities. These results are discussed in the context of a mean-field treatment of anyons on a lattice.