Superconductivity in a system of interacting spinful semions

Non-interacting particles obeying certain fractional statistics have been predicted to exhibit superconductivity. We discuss the issue in an attractively interacting system of spinful semions on a lattice by numerically investigating the presence of off-diagonal long-range order at zero temperature. For this purpose, we construct a Hubbard model wherein two semions with opposite spin can virtually coincide while maintaining consistency with the fractional braiding statistics. Clear off-diagonal long range order is seen in the strong coupling limit, consistent with the expectation that a pair of semions obeys Bose statistics. We find that the semion system behaves similarly to a system of fermions with the same attractive Hubbard $U$ interaction for a wide range of $U$, suggesting that semions also undergo a BCS to BEC crossover as a function of $U$.