Z_2-slave-spin theory for strongly correlated fermions

TL;DR

This paper reviews a Z_2-slave-spin representation of Hubbard-like models, exploring mean-field and cluster approximations to understand metal-insulator transitions and spectral properties in strongly correlated fermions.

Contribution

It introduces a Z_2-slave-spin framework for Hubbard models, linking mean-field Hubbard bands to an Ising model in a transverse field and incorporating non-local correlations.

Findings

Hubbard bands derived from Ising model excitations

Quantum critical point linked to Brinkman-Rice transition

Cluster mean-field captures non-local correlations

Abstract

We review a representation of Hubbard-like models that is based on auxiliary pseudospin variables. These pseudospins refer to the local charge modulo two in the original model and display a local Z_2 gauge freedom. We discuss the associated mean-field theory in a variety of different contexts which are related to the problem of the interaction-driven metal-insulator transition at half-filling including Fermi surface deformation and spectral features beyond the local approximation. Notably, on the mean-field level, the Hubbard bands are derived from the excitations of an Ising model in a transverse field and the quantum critical point of this model is identified with the Brinkman-Rice criticality of the almost localized Fermi liquid state. Non-local correlations are included using a cluster mean-field approximation and the Schwinger boson theory for the auxiliary quantum Ising model.