Numerical analysis of correlation effects in the Josephson current through a quantum dot

We have performed a quantum Monte-Carlo calculation for the DC Josephson current through a quantum dot. Electron Green's functions dressed by a short range repulsion U on the dot were obtained by the Hirsch-Fye algorithm. Temperature dependence of the Josephson current was determined for a junction made of a single dot connected with two d-wave superconductors. Our calculation reproduced a double-peaked spectral function and change in the sign of the current when the Coulomb blockade occurred at low temperatures. Indication of resonant tunneling was seen in the current, when the chemical potential on the dot was shifted by about U/2 from the band center.