Two-Particle Self-Consistent method for the multi-orbital Hubbard model

TL;DR

This paper reviews the extension of the Two-Particle Self-Consistent (TPSC) method to multi-orbital Hubbard models, providing a non-perturbative approach for analyzing electronic correlations in complex solid state systems.

Contribution

It introduces a detailed derivation of the multi-orbital generalization of TPSC and compares its features with dynamical mean-field theory results.

Findings

TPSC effectively describes electronic correlations in multi-orbital systems.

Comparison shows TPSC captures key features similar to dynamical mean-field theory.

The method offers a non-perturbative alternative for complex models.

Abstract

One of the most challenging problems in solid state systems is the microscopic analysis of electronic correlations. A paramount minimal model that encodes correlation effects is the Hubbard Hamiltonian, which -- albeit its simplicity -- is exactly solvable only in a few limiting cases and approximate many-body methods are required for its solution. In this review we present an overview on the non-perturbative Two-Particle Self-Consistent method (TPSC) which was originally introduced to describe the electronic properties of the single-band Hubbard model. We introduce here a detailed derivation of the multi-orbital generalization of TPSC and discuss particular features of the method on exemplary interacting models in comparison to dynamical mean-field theory results.