Phase diagrams of correlated electrons: systematic corrections to the mean field theory

TL;DR

This paper develops a systematic correction scheme to mean field theory for correlated electron systems, enabling unbiased comparison of instabilities and applying it to the Hubbard model to map out phase stability.

Contribution

It introduces a perturbative correction method equivalent to a variational approach, allowing consistent analysis of particle-hole and particle-particle instabilities in correlated electrons.

Findings

Antiferromagnetic and d-wave Pomeranchuk phases are stable near half filling at Van Hove density.

d-wave superconductivity dominates away from the singular filling.

The method provides a detailed phase diagram of the t-t' Hubbard model.

Abstract

Perturbative corrections to the mean field theory for particle-hole instabilities of interacting electron systems are computed within a scheme which is equivalent to the recently developed variational approach to the Kohn-Luttinger superconductivity. This enables an unbiased comparison of particle-particle and particle-hole instabilities within the same approximation scheme. A spin-rotation invariant formulation for the particle-hole instabilities in the triplet channel is developed. The method is applied to the phase diagram of the t-t' Hubbard model on the square lattice. At the Van Hove density, antiferromagnetic and d-wave Pomeranchuk phases are found to be stable close to half filling. However, the latter phase is confined to an extremely narrow interval of densities and away from the singular filling, d-wave superconducting instability dominates.