# Analytical slave-spin mean-field approach to orbital selective Mott insulators

## TL;DR

This paper develops an analytical slave-spin mean-field approach to study orbital-selective Mott insulators in multi-orbital Hubbard models, providing insights into phase transitions and the method's limitations.

## Contribution

It introduces an analytical framework for understanding orbital-selective Mott transitions using slave-spin mean-field theory, including Landau-Ginzburg formulation and impurity-lattice correspondence.

## Key findings

- Formulation of orbital locking and selective Mott transition within Landau-Ginzburg theory.
- Analysis of the stability of orbital-selective Mott phase against hybridization.
- Identification of limitations of the slave-spin method for inter-orbital tunneling in multi-orbital systems.

## Abstract

We use the slave-spin mean-field approach to study particle-hole symmetric one- and two-band Hubbard models in presence of Hund's coupling interaction. By analytical analysis of Hamiltonian, we show that the locking of the two orbitals vs.\,orbital-selective Mott transition can be formulated within a Landau-Ginzburg framework. By applying the slave-spin mean-field to impurity problem, we are able to make a correspondence between impurity and lattice. We also consider the stability of the orbital selective Mott phase to the hybridization between the orbitals and study the limitations of the slave-spin method for treating inter-orbital tunnellings in the case of multi-orbital Bethe lattices with particle-hole symmetry.