Non-Fermi liquid theory of a compactified Anderson single-impurity model

TL;DR

This paper develops a non-Fermi liquid theory for a compactified Anderson impurity model, using Majorana fermions and perturbation theory, revealing a new low-temperature scale and insights into resistivity, specific heat, and pairing susceptibilities.

Contribution

It introduces a novel perturbative approach using Pfaffian determinants in the Majorana fermion representation for the compactified Anderson model, identifying a new weak-coupling low-temperature scale.

Findings

Linear temperature dependence of resistivity.

Logarithmic corrections to specific heat and susceptibilities.

Discovery of a new low-temperature energy scale T_c.

Abstract

We consider a version of the symmetric Anderson impurity model (compactified) which has a non-Fermi liquid weak coupling regime. We find that in the Majorana fermion representation, perturbation theory can be conveniently developed in terms of Pfaffian determinants and we use this formalism to calculate the impurity free energy, self energies, and vertex functions. In the second-order perturbation theory, a linear temperature dependence of electrical resistivity is obtained, and the leading corrections to the impurity specific heat are found to behave as $T\ln T$. The impurity susceptibilities have terms in $\ln T$ to zero, first, and second order, and corrections of $\ln^2 T$ to second order as well. The singlet superconducting paired susceptibility at the impurity site, is found to have second-order corrections $\ln T$, which we interpret as an indication that a singlet conduction electron pairing resonance forms at the Fermi level. When the perturbation theory is extended to third order logarithmic divergences are found in the vertex function $\Gamma_{0,1,2,3}(0,0,0,0)$. Multiplicative renormalization-group method is then used to sum all the leading order logarithmic contributions, giving rise to a new weak-coupling low-temperature energy scale $T_c=\Delta{\rm exp}\left[-\frac{1}{9}\left(\frac{\pi\Delta}{U} \right )^{2}\right]$. The scaling equation shows the dimensionless coupling constant $\frac{U}{\pi\Delta}$ is increased as the energy scale $\Delta$ reduces. Our perturbational results can be justified only in the regime $T>T_c$.