New Solutions of the T-Matrix Theory of the Attractive Hubbard Model

TL;DR

This paper introduces a highly accurate computational method for analyzing dynamical properties in many-body theories, demonstrated on the attractive Hubbard model, revealing pseudogap development at lower temperatures.

Contribution

It presents a novel calculational approach using partial fraction decomposition and computer algebra to precisely solve T-matrix theories without analytical continuation errors.

Findings

High-precision calculation of pair propagator residues and poles.

Clear evidence of pseudogap formation as temperature decreases.

Method achieves relative error of 10^(-80) in key quantities.

Abstract

This short paper summarizes a calculational method for obtaining the dynamical properties of many-body theories formulated in terms of (unrenormalized) bare propagators (and more generally, in terms of meromorphic functions, or convolutions over meromorphic functions) to a very high accuracy. We demonstrate the method by applying it to a T-matrix theory of the attractive Hubbard model in two dimensions. We expand the pair propagator using a partial fraction decomposition, and then solve for the residues and pole locations of such a decomposition using a computer algebra system to an arbitrarily high accuracy (we used MapleV and obtained these quantities to a relative error of 10^(-80)). Thus, this method allows us to bypass all inaccuracies associated with the traditional analytical continuation problem. Our results for the density of states make clear the pronounced development of a pseudogap as the temperature is lowered in this formulation of the attractive Hubbard model.