Numerical study of transport through a single impurity in a spinful Tomonaga-Luttinger liquid

TL;DR

This study uses path-integral Monte Carlo methods to analyze charge and spin conductance in a spinful Tomonaga-Luttinger liquid with an impurity, revealing complex phase behavior beyond standard RG predictions.

Contribution

It provides a detailed numerical phase diagram for impurity effects in a spinful Tomonaga-Luttinger liquid, highlighting deviations from traditional RG analysis and offering new insights into conductance phases.

Findings

Identified four distinct conductance phases at low temperatures.

Phase boundaries interpolate between weak and strong scattering limits.

Some phase boundary behaviors are not fully explained by standard RG theory.

Abstract

The single impurity problem in a spinful Tomonaga-Luttinger liquid is studied numerically using path-integral Monte Carlo methods. The advantage of our approach is that the system allows for extensive analyses of charge and spin conductance in the non-perturbative regime. By closely examining the behavior of conductances at low temperatures, in the presence of a finite backward scattering barrier due to the impurity, we identified four distinct phases characterized by either perfect transmission or reflection of charge and spin channels. Our phase diagram for an intermediate scattering strength is consistent with the standard perturbative renormalization group (RG) analysis in the limit of weak and strong backward scattering, in the sense that all our phase boundaries interpolate the two limiting cases. Further investigations show, however, that precise location and form of our phase boundaries are not trivially explained by the standard RG analysis, e.g., some part of the phase diagram looks much similar to the weak backscattering limit, whereas some other part is clearly derived from the opposite limit. In order to give a more intuitive interpretation of such behaviors, we also reconsidered our impurity problem from the viewpoint of a quantum Brownian motion picture.