Phase Fluctuations in Strongly Coupled d-Wave Superconductors

We present a numerically exact solution for the BCS Hamiltonian at any temperature, including the degrees of freedom associated with classical phase, as well as amplitude fluctuations via a Monte Carlo integration. This allows for an investigation over the whole range of couplings: from weak attraction, as in the well-known BCS limit, to the mainly unexplored strong-coupling regime of pronounced phase fluctuations. In the latter, two characteristic temperatures T$^*$ and T$_c$, associated with short- and long-range ordering, respectively, can be identified in a mean-field-motivated Hamiltonian. T$^*$ at the same time corresponds to the opening of a gap in the excitation spectrum. In addition to introducing a novel procedure to study strongly coupled $d$-wave superconductors, our results indicate that classical phase fluctuations are not sufficient to explain the pseudogap features of high-temperature superconductors.