U(1) Slave-spin theory and its application to Mott transition in a multi-orbital model for iron pnictides

TL;DR

This paper introduces a U(1) slave-spin theory for multi-orbital Hubbard models, effectively capturing Mott transitions and strongly correlated metallic phases in iron pnictides, with advantages over previous approaches in non-degenerate systems.

Contribution

The paper develops a U(1) slave-spin approach that accurately describes Mott physics in multi-orbital models, especially for non-degenerate orbitals, and applies it to iron pnictides.

Findings

Demonstrates a Mott transition in a five-orbital model for iron pnictides.

Identifies a crossover from weakly to strongly correlated metal influenced by Hund's coupling.

Finds nearly degenerate orbital selective Mott state near the transition.

Abstract

A U(1) slave-spin representation is introduced for multi-orbital Hubbard models. As with the $Z_2$ form of L. de'Medici et al. (Phys. Rev. B 72, 205124 (2005)), this approach represents a physical electron operator as the product of a slave spin and an auxiliary fermion operator. For non-degenerate multi-orbital models, our U(1) approach is advantageous in that it captures the non-interacting limit at the mean-field level. For systems with either a single orbital or degenerate multiple orbitals, the U(1) and $Z_2$ slave-spin approachs yield the same results in the slave-spin-condensed phase. In general, the U(1) slave-spin approach contains a U(1) gauge redundancy, and properly describes a Mott insulating phase. We apply the U(1) slave-spin approach to study the metal-to-insulator transition in a five-orbital model for parent iron pnictides. We demonstrate a Mott transition as a function of the interactions in this model. The nature of the Mott insulating state is influenced by the interplay between the Hund's rule coupling and crystal field splittings. In the metallic phase, when the Hund's rule coupling is beyond a threshold, there is a crossover from a weakly correlated metal to a strongly correlated one, through which the quasiparticle speactral weight rapidly drops. The existence of such a strongly correlated metallic phase supports the incipient Mott picture of the parent iron pnictides. In the parameter regime for this phase and in the vicinity of the Mott transition, we find that an orbital selective Mott state has nearly as competitive a ground state energy.