The Two-Particle Self-Consistent Approach for Multiorbital models: application to the Emery model

TL;DR

This paper extends the two-particle self-consistent (TPSC) approach to multiorbital models, specifically applying it to the Emery model to better understand spin fluctuations and correlation effects in cuprate superconductors.

Contribution

It introduces a TPSC+DMFT framework for the Emery model, incorporating interacting orbital densities and analyzing spin fluctuation vertex behavior.

Findings

Vertex for spin fluctuations decreases with filling at constant U

Interacting orbital densities are essential for accurate calculations

Potential explanation for differences in correlation in electron- and hole-doped cuprates

Abstract

The Emery model, or three-band Hubbard model, is a Hamiltonian that is thought to contain much of the physics of cuprate superconductors. This model includes two noninteracting $p$ orbitals and one interacting $d$ orbital per unit cell. Few methods that can solve multiorbital interacting Hamiltonians reliably and efficiently exist. Here, we introduce an application of the two particle self-consistent (TPSC) approach to the Emery model. We construct this method within the framework of the TPSC+DMFT method, which can be seen as a way to introduce nonlocal corrections to dynamical mean-field theory (DMFT). We show that interacting orbital densities, rather than the noninteracting ones, must be used in the calculations. For the Emery model, we find that at constant bare interaction $U$, the vertex for spin fluctuations, $U_{sp}$, decreases rapidly with filling. This may be one of the factors that contributes to electron-doped cuprates appearing less correlated than hole-doped ones. More generally, our work opens the road to the application of the TPSC approach to spin fluctuations in multiorbital models.