Fermi and non-Fermi liquid behavior in quantum impurity systems: Conserving slave boson theory

TL;DR

This paper develops a conserving slave boson approach to analyze Fermi and non-Fermi liquid behaviors in Anderson impurity models, accurately capturing low-energy excitations and infrared properties.

Contribution

It introduces a conserving T-matrix approximation that preserves gauge symmetry and correctly describes both Fermi and non-Fermi liquid regimes in impurity systems.

Findings

The CTMA incorporates all leading and subleading infrared singularities.

The method accurately reproduces the infrared behavior of auxiliary particle propagators.

It provides a unified framework for Fermi and non-Fermi liquid regimes.

Abstract

The question of Fermi liquid vs. non-Fermi liquid behavior induced by strong correlations is one of the prominent problems in metallic local moment systems. As standard models for such systems, the SU(N)xSU(M) Anderson impurity models exhibit both Fermi liquid and non-Fermi liquid behavior, depending on their symmetry. Taking the Anderson model as an example, these lectures first give an introduction to the auxiliary boson method to describe correlated systems governed by a strong, short-range electronic repulsion. It is then shown how to include the relevant low-lying excitations (coherent spin flip and charge fluctuation processes), while preserving the local gauge symmetry of the model. This amounts to a conserving T-matrix approximation (CTMA). We prove a cancellation theorem showing that the CTMA incorporates all leading and subleading infrared singularities at any given order in a self-consistent loop expansion of the free energy. As a result, the CTMA recovers the correct infrared behavior of the auxiliary particle propagators, indicating that it correctly describes both the Fermi and the non-Fermi regimes of the Anderson model.