Particle-hole Symmetric Slave Boson Method for the Mixed Valence Problem

TL;DR

This paper presents an analytic slave boson method for the finite U Anderson impurity model, capturing valence fluctuations and Kondo physics within a unified framework that simplifies the treatment of high and low energy regimes.

Contribution

It introduces a symmetric s-boson approach that encodes atomic physics and unifies slave rotor and s-boson representations for the Anderson model.

Findings

Recovers infinite U and Kondo limit actions

Shows Kondo resonance develops before slave boson condensation

Establishes a unified framework connecting different slave boson methods

Abstract

We introduce an analytic slave boson method for treating the finite $U$ Anderson impurity model. Our approach introduces two bosons to track both $Q\rightleftharpoons Q\pm1$ valence fluctuations and reduces to a single symmetric $s$-boson in the effective action, encoding all the high energy atomic physics information in the boson's kinematics, while the low energy part of the action remains unchanged across finite $U$, infinite $U$, and Kondo limits. We recover the infinite $U$ and Kondo limit actions from our approach and show that the Kondo resonance already develops in the normal state when the slave boson has yet to condense. We show that the slave rotor and $s$-boson have the same algebraic structure, and we establish a unified functional integral framework connecting the $s$-boson and slave rotor representations for the single impurity Anderson model.