Demonstration of a robust pseudogap in a three-dimensional correlated electronic system

TL;DR

This paper introduces a new computational method to analyze the pseudogap phenomenon in a three-dimensional correlated electronic system, demonstrating its effectiveness on the attractive Hubbard model and revealing persistent pseudogaps at various couplings.

Contribution

The paper presents a partial-fractions decomposition method for accurately calculating spectral functions and density of states, and applies it to show the existence of a robust pseudogap in three-dimensional systems.

Findings

A pseudogap persists over a large temperature range at intermediate coupling.

In three dimensions, the pseudogap remains finite in the thermodynamic limit.

The pseudogap energy at Tc is significantly larger than the zero-temperature BCS gap at intermediate coupling.

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 Tc 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 this approximation to represent a true continuous phase transition, and in the thermodynamic limit any pseudogap predicted by this formulation will remain finite. We have applied our method to the attractive Hubbard model on a three-dimensional simple cubic lattice, and find 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 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 BCS gap energies are essentially equal.