Manumitting slave-spins in the Anderson impurity model

TL;DR

This paper presents an exact mapping of the Anderson impurity model to a resonant level model with Ising variables, providing a stable mean-field solution that accurately captures the Kondo regime's Wilson ratio.

Contribution

It introduces a novel exact mapping of the Anderson model to a resonant level model with Ising variables, improving mean-field stability and accuracy.

Findings

Mean-field solution is stable against unphysical magnetization.

Wilson ratio approaches the exact value in the Kondo regime.

Mapping simplifies analysis of asymmetric Anderson models.

Abstract

We show that a generic single-orbital Anderson impurity model, lacking for instance any kind of particle-hole symmetry, can be exactly mapped without any constraint onto a resonant level model coupled to two Ising variables, which reduce to one if the hybridisation is particle-hole symmetric. The mean-field solution of this model is found to be stable to unphysical spontaneous magnetisation of the impurity, unlike the saddle-point solution in the standard slave-boson representation. Remarkably, the mean-field estimate of the Wilson ratio approaches the exact value $R_\text{W}=2$ in the Kondo regime.