Slave-spin mean field for broken-symmetry states: N\'eel antiferromagnetism and its phase separation in multi-orbital Hubbard models

TL;DR

This paper extends the slave-spin mean-field method to include broken-symmetry phases, applying it to study antiferromagnetism and phase separation in multi-orbital Hubbard models, revealing the effects of Hund's coupling.

Contribution

It generalizes the slave-spin mean-field approach to broken-symmetry states and demonstrates its equivalence to other methods, applying it to complex multi-orbital systems.

Findings

Doped antiferromagnet is unstable towards phase separation.

Hund's coupling extends antiferromagnetic stability and promotes phase separation.

The formalism produces results consistent with Kotliar-Ruckenstein slave-bosons and Gutzwiller approximation.

Abstract

We introduce the generalization of the Slave-Spin Mean-Field method to broken-symmetry phases. Through a variational approach we derive the single-particle energy shift in the mean-field equations which generates the appropriate self-consistent field responsible for the stabilization of the broken symmetry. With this correction the different flavours of the slave-spin mean-field are actually the same method and they give identical results to Kotliar-Ruckenstein slave-bosons and to the Gutzwiller approximation. We apply our formalism to the N\'eel antiferromagnetic state and study it in multi-orbital models as a function of the number of orbitals and Hund's coupling strength, providing phase diagrams in the interaction-doping plane. We show that the doped antiferromagnet in proximity of half-filling is typically unstable towards insulator-metal and magnetic-non magnetic phase separation. Hund's coupling extends the range of this antiferromagnet, and favors its phase separation.