Junctions of one-dimensional quantum wires - correlation effects in transport

TL;DR

This paper studies how spinless fermions transport through a quantum wire junction with interactions, using the functional renormalization group to analyze conductance behavior and fixed points.

Contribution

It applies the functional renormalization group to analyze transport and fixed points in multi-wire quantum junctions with interactions, providing new insights into their low-energy physics.

Findings

Identification of multiple fixed points and their stability.

Determination of scaling exponents near fixed points.

Some results align with Hartree-Fock approximation.

Abstract

We investigate transport of spinless fermions through a single site dot junction of M one-dimensional quantum wires. The semi-infinite wires are described by a tight-binding model. Each wire consists of two parts: the non-interacting leads and a region of finite extent in which the fermions interact via a nearest-neighbor interaction. The functional renormalization group method is used to determine the flow of the linear conductance as a function of a low-energy cutoff for a wide range of parameters. Several fixed points are identified and their stability is analyzed. We determine the scaling exponents governing the low-energy physics close to the fixed points. Some of our results can already be derived using the non-self-consistent Hartree-Fock approximation.