Two-Particle-Self-Consistent Approach for the Hubbard Model

TL;DR

The paper presents the Two-Particle-Self-Consistent (TPSC) approach for the Hubbard model, which respects key physical principles and provides insights into pseudogap formation and d-wave superconductivity in two dimensions.

Contribution

It introduces and reviews the TPSC method, a novel approach that satisfies fundamental physical constraints and offers a reliable framework for studying the Hubbard model.

Findings

TPSC respects the Mermin-Wagner theorem and sum rules.

It explains pseudogap formation when correlation length exceeds thermal wavelength.

Conditions for d-wave superconductivity are analyzed within TPSC.

Abstract

Even at weak to intermediate coupling, the Hubbard model poses a formidable challenge. In two dimensions in particular, standard methods such as the Random Phase Approximation are no longer valid since they predict a finite temperature antiferromagnetic phase transition prohibited by the Mermin-Wagner theorem. The Two-Particle-Self-Consistent (TPSC) approach satisfies that theorem as well as particle conservation, the Pauli principle, the local moment and local charge sum rules. The self-energy formula does not assume a Migdal theorem. There is consistency between one- and two-particle quantities. Internal accuracy checks allow one to test the limits of validity of TPSC. Here I present a pedagogical review of TPSC along with a short summary of existing results and two case studies: a) the opening of a pseudogap in two dimensions when the correlation length is larger than the thermal de Broglie wavelength, and b) the conditions for the appearance of d-wave superconductivity in the two-dimensional Hubbard model.