Temperature derivative of the superfluid density in the attractive Hubbard model

Based on extensions of the grand-canonical quantum Monte Carlo algorithm to incorporate magnetic fields, we provide numerical data confirming the existence of a Kosterlitz-Thouless transition in the attractive Hubbard model. Here, we calculate the temperature derivative of the superfluid density, [∂β${\mathit{D}}_{\mathit{s}}$(β)]/∂β, to pin down the transition. The latter quantity is obtained from the difference in internal energy of systems which differ by a phase twist π/2 in the boundary condition along one lattice direction. Away from half-band filling, [∂β${\mathit{D}}_{\mathit{s}}$(β)]/∂β shows a response which increases with lattice size at the transition temperature. In contrast, such a signal is not observed at half-band filling.