Functional Renormalization-Group Analysis of Luttinger Liquids with Impurities

TL;DR

This paper uses the functional renormalization group to analyze how impurities affect spectral and transport properties in Luttinger liquids, revealing complex crossover behaviors and the importance of energy scales in one-dimensional quantum systems.

Contribution

It applies the fRG method to study impurity effects in Luttinger liquids, capturing crossover phenomena and energy scale dependencies beyond low-energy fixed point approximations.

Findings

Impurities cause crossover phenomena in spectral and transport properties.

Asymptotic behaviors are only reached at very low energy scales for weak and intermediate impurities.

Two-particle backscattering significantly alters spectral weight and conductance, with logarithmic corrections.

Abstract

In one-dimensional quantum wires the interplay of electron correlations and impurities strongly influences the low-energy physics. The diversity of energy scales and the competition of correlations in interacting Fermi systems can be treated very efficiently with the functional renormalization group (fRG), describing the gradual evolution from a microscopic model Hamiltonian to the effective low-energy action as a function of a continuously decreasing energy cutoff. The fRG provides the universal low-energy asymptotics as well as nonuniversal properties, and in particular an answer to the important question at what scale the ultimate asymptotics sets in. We investigate the influence of impurities on spectral and transport properties of fermionic lattice models with short-range interactions. The results capture relevant energy scales and crossover phenomena, in addition to the universal low-energy asymptotics. For weak and intermediate impurity strengths the asymptotic behavior is approached only at rather low energy scales, accessible only for very large systems. For spin-1/2 systems two-particle backscattering leads to striking effects, which are not captured if the bulk system is approximated by its low-energy fixed point, the Luttinger model. In particular, the expected decrease of spectral weight near the impurity and of the conductance at low energy scales is often preceded by a pronounced increase, and the asymptotic power laws are modified by logarithmic corrections.