Temperature derivative of the superfluid density in the attractive Hubbard model.

Abstract

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, [\ensuremath{\partial}\ensuremath{\beta}${\mathit{D}}_{\mathit{s}}$(\ensuremath{\beta})]/\ensuremath{\partial}\ensuremath{\beta}, to pin down the transition. The latter quantity is obtained from the difference in internal energy of systems which differ by a phase twist \ensuremath{\pi}/2 in the boundary condition along one lattice direction. Away from half-band filling, [\ensuremath{\partial}\ensuremath{\beta}${\mathit{D}}_{\mathit{s}}$(\ensuremath{\beta})]/\ensuremath{\partial}\ensuremath{\beta} shows a response which increases with lattice size at the transition temperature. In contrast, such a signal is not observed at half-band filling.