Scaling and criticality of the Kondo effect in a Luttinger liquid

TL;DR

This study uses a quantum Monte Carlo method to explore the critical behavior of a Kondo impurity in a Luttinger liquid across all temperatures, revealing different regimes of Fermi-liquid and anomalous power-law behavior.

Contribution

Developed a numerically exact quantum Monte Carlo simulation to analyze the Kondo effect in a Luttinger liquid without finite-size limitations.

Findings

Fermi-liquid behavior for g_c < 1/2 in strong interactions

Anomalous power laws for 1/2 < g_c < 1

Logarithmic divergence with potential scattering at g_c < 1/2

Abstract

A quantum Monte Carlo simulation method has been developed and applied to study the critical behavior of a single Kondo impurity in a Luttinger liquid. This numerically exact method has no finite-size limitations and allows to simulate the whole temperature range. Focusing on the impurity magnetic susceptibility, we determine the scaling functions, in particular for temperatures well below the Kondo temperature. In the absence of elastic potential scattering, we find Fermi-liquid behavior for strong electron-electron interactions, g_c < 1/2, and anomalous power laws for 1/2<g_c < 1, where g_c is the correlation parameter of the Luttinger liquid. These findings resolve a recent controversy. If elastic potential scattering is present, we find a logarithmically divergent impurity susceptibility at g_c<1/2 which can be rationalized in terms of the two-channel Kondo model.