Dynamical Properties of the Anderson Impurity Model within a Diagrammatic Pseudoparticle Approach

TL;DR

This paper extends the Conserving T-Matrix Approximation to study the Anderson Impurity Model, successfully capturing Fermi liquid behavior in the single-channel case and non-Fermi liquid features in the two-channel case, with implications for strongly correlated systems.

Contribution

The authors develop an extended CTMA approach for the Anderson model, accurately describing both Fermi liquid and non-Fermi liquid regimes in different channel configurations.

Findings

Single-channel case shows temperature-independent spin susceptibility below T_K.

Impurity spectral density remains non-singular at low temperatures.

Two-channel case exhibits power-law singularity in spectral density, indicating non-Fermi liquid behavior.

Abstract

The Anderson model of a twofold spin degenerate impurity level in the limit of infinite Coulomb repulsion, $U \to \infty$, coupled to one and two degenerate conduction bands or channels, is considered in pseudo-particle representation. We extend the Conserving T-Matrix Approximation (CTMA), a general diagrammatic approximation scheme based on a fully renormalized computation of two-particle vertex functions in the spin and in the charge channel, to the calculation of thermodynamic and spectral properties. In the single-channel case, the CTMA yields in the Kondo regime a temperature independent Pauli spin susceptibility for temperatures below the Kondo temperature $T_K$ and down to the lowest temperatures considered, reproducing the exact spin screening in the Fermi liquid state. The impurity spectral density appears to remain non-singular down to the lowest temperatures, in agreement with Fermi liquid behavior. However, the unitarity sum rule, which is crucial for an impurity solver like the CTMA to be applicable within Dynamical Mean Field Theories for strongly correlated lattice models, is overestimated at the lowest temperatures. We argue that this shortcoming may be due to numerical imprecision and discuss an appropriate scheme for its correction. In the two-channel case, the spectral density calculated within CTMA exhibit qualitatively the correct non-Fermi liquid behavior at low temperatures, i.e. a powerlaw singularity.