Prospects for Non--Fermi--Liquid Behavior of a Two Level Impurity in a Metal

TL;DR

This paper investigates the potential for non-Fermi-liquid behavior in a two-site impurity system within a metal, revealing that additional tunnelling processes tend to suppress such behavior, making it unlikely under typical conditions.

Contribution

It demonstrates that extra tunnelling processes prevent the realization of non-Fermi-liquid fixed points in a two-site impurity model, providing a detailed analysis of the conditions needed for such behavior.

Findings

Extra tunnelling processes drive the system away from non-Fermi-liquid fixed points.

Achieving non-Fermi-liquid behavior requires fine-tuning of tunnelling terms.

A new multicritical non-Fermi-liquid fixed point is identified.

Abstract

It has been claimed that an impurity hopping between two sites in a metal can lead to non--Fermi liquid behavior if the bias between the two sites is tuned to zero. Here it is shown that several extra tunnelling processes are allowed; those involving bare impurity tunnelling as well as two--electron--assisted tunnelling play important roles. These terms generally drive the system away from the intermediate coupling non--Fermi--liquid fixed point, which has the character of the two channel Kondo problem. In order to find the non-Fermi liquid behavior a combination of these terms must be small over a range of energy scales. The prospects for obtaining these conditions are studied by analyzing both the weak coupling and the intermediate coupling behavior, together with the connecting crossover region. Unfortunately, the conclusions are rather pessimistic. The phase diagram and the important crossover are analyzed via bosonization and refermionization and some of the results compared to those obtained from conformal field theory. Finally, an additional non-Fermi liquid fixed point is found, a multicritical point with two relevant directions even in the unbiased case.