Two-Particle Self-Consistent Method For The Multi-Orbital Hubbard Model

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-regardless of its simplicity-is exactly solvable only in a few limiting cases and approximate many-body methods are required for its solution. In this review, 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, is presented. A detailed derivation of the multi-orbital generalization of TPSC is introduced here and particular features of the method on exemplary interacting models in comparison to dynamical mean-field theory results are discussed.