Pairing Fluctuations in The Attractive Hubbard Model in the Atomic Limit

TL;DR

This paper investigates pairing fluctuations in the attractive Hubbard model at the atomic limit, comparing different self-consistent T-matrix approaches and a TPSC method, identifying the most accurate approximation in the strong coupling regime.

Contribution

It critically evaluates various self-consistent T-matrix methods and TPSC in the strong coupling limit, providing insights into their accuracy and applicability.

Findings

One self-consistency degree is highly accurate at low temperatures.

The T-matrix approximation's effectiveness varies with self-consistency level.

The study offers guidance on choosing appropriate methods for strong coupling regimes.

Abstract

BCS theory accounts for the pairing instability in the weak coupling limit, but fails to describe pairing fluctuations above $T_c$. One possibility for describing these fluctuations in the dilute limit is the T-matrix approximation. We critically examine various degrees of self-consistency in the T-matrix formalism, along with a non-diagrammatic two-particle self-consistent (TPSC) formulation, in the strong coupling regime, where an exact solution is readily available. We find that one particular degree of self-consistency is quite accurate, particularly at low temperature as evidenced by examining both static and dynamic properties.