Demonstration of a Robust Pseudogap in a Three-Dimensional Correlated Electronic System

Abstract

We outline a partial-fractions decomposition method for determining the one-particle spectral function and single-particle density of states of a correlated electronic system on a finite lattice in the non self-consistent T-matrix approximation to arbitrary numerical accuracy, and demonstrate the application of these ideas to the attractive Hubbard model. We then demonstrate the effectiveness of a finite-size scaling ansatz which allows for the extraction of quantities of interest in the thermodynamic limit from this method. In this approximation, in one or two dimensions, for any finite lattice or in the thermodynamic limit, a pseudogap is present and its energy diverges as T c is approached from above; this is an unphysical manifestation of using an approximation that predicts a spurious phase transition in one or two dimensions. However, in three dimensions one expects the transition predicted by the approximation to represent a true continuous phase transition, and whether or not a pseudo gap exists in the thermodynamic limit in three dimensions remains an open question. We have applied our method to the attractive Hubbard model on a three-dimensional simple cubic lattice, and find, similar to previous work, that for intermediate coupling a prominent pseudogap is found in the single-particle density of states, and this gap persists over a large temperature range. In addition, we also show that for weak coupling (an on-site Hubbard energy equal to one quarter the bandwidth) a pseudogap is also present. The pseudogap energy at the transition temperature is almost a factor of three larger than the T = 0 BCS gap for intermediate coupling, whereas for weak coupling the pseudogap and T = 0 BCS gap energies are essentially equal. These results show that a pseudogap due to superconducting fluctuations occurs in three dimensions even in the weak-coupling limit.