Multi-orbital simplified parquet equations for strongly correlated electrons

TL;DR

This paper develops a simplified parquet equation approach for multi-orbital strongly correlated electron systems, enabling efficient analysis of metal-insulator transitions and Fermi liquid behavior within the dynamical mean-field framework.

Contribution

It extends a previous single-impurity approximation to multi-orbital models, providing a computationally manageable method to study complex electron interactions.

Findings

Describes multi-orbital models with large matrices within the approximation.

Shows the model is a Fermi liquid in the metallic phase.

Analyzes metal-insulator transition driven by crystal field effects.

Abstract

We extend an approximation earlier developed by us for the single-impurity Anderson model to a full-size impurity solver for models of interacting electrons with multiple orbitals. The approximation is based on parquet equations simplified by separating small and large energy fluctuations justified in the critical region of a pole in the two-particle vertex. We show that an $l$-orbital model with most general interaction is described within this approximation by $4l^{2}\times 4l^{2}$ matrices and is Fermi liquid in the metallic phase. We explicitly calculate properties of a paramagnetic solution of a two-orbital Hubbard model with a Hund exchange and orbital splitting within the dynamical mean-field approximation. We trace the genesis of a metal-insulator transition induced by a crystal field and vanishing of the Kondo quasiparticle peak in strongly correlated orbitally asymmetric systems.