Transport of interacting electrons through a potential barrier: nonperturbative RG approach

TL;DR

This paper develops a nonperturbative renormalization group approach to calculate the temperature-dependent conductance of interacting electrons in a Luttinger liquid with a potential barrier, providing a comprehensive analytical solution.

Contribution

It introduces a nonperturbative RG method for arbitrary interactions and barrier strengths, extending previous perturbative analyses of electron transport in Luttinger liquids.

Findings

Derived an analytical RG equation for conductance as a function of temperature.

Summed ladder series to all orders in interaction strength g_2.

Results agree with known limiting cases, validating the approach.

Abstract

We calculate the linear response conductance of electrons in a Luttinger liquid with arbitrary interaction g_2, and subject to a potential barrier of arbitrary strength, as a function of temperature. We first map the Hamiltonian in the basis of scattering states into an effective low energy Hamiltonian in current algebra form. Analyzing the perturbation theory in the fermionic representation the diagrams contributing to the renormalization group (RG) \beta-function are identified. A universal part of the \beta-function is given by a ladder series and summed to all orders in g_2. First non-universal corrections beyond the ladder series are discussed. The RG-equation for the temperature dependent conductance is solved analytically. Our result agrees with known limiting cases.