Functional Integral Approach to the Single Impurity Anderson Model

TL;DR

This paper applies a novel functional integral method with spin-dependent Bose fields to analyze the single impurity Anderson model, focusing on Green's functions and susceptibilities in different regimes, and compares results with NCA calculations.

Contribution

It introduces a functional integral approach with strict no-double-occupancy constraints for the Anderson model, providing new computational insights.

Findings

Calculated f-electron Green's function and susceptibility in Kondo and mixed-valence regimes

Identified challenges in extracting spectral functions from imaginary time data

Compared results with Non-Crossing Approximation (NCA) calculations

Abstract

Recently, a functional integral representation was proposed by Weller (Weller, W.: phys.~stat.~sol.~(b) {\bf 162}, 251 (1990)), in which the fermionic fields strictly satisfy the constraint of no double occupancy at each lattice site. This is achieved by introducing spin dependent Bose fields. The functional integral method is applied to the single impurity Anderson model both in the Kondo and mixed-valence regime. The f-electron Green's function and susceptibility are calculated using an Ising-like representation for the Bose fields. We discuss the difficulty to extract a spectral function from the knowledge of the imaginary time Green's function. The results are compared with NCA calculations.