Features of renormalization induced by interaction in 1D transport

TL;DR

This paper investigates how interaction differences between a 1D quantum wire and reservoirs affect charge correlations and renormalization of physical quantities, revealing that shot noise charge is determined by reservoir properties while susceptibilities are influenced by wire interactions.

Contribution

It introduces a theoretical analysis of the renormalization effects induced by interaction differences in 1D transport, highlighting the distinct roles of the interaction constants in reservoirs and the wire.

Findings

Charge in shot noise is determined by reservoir interaction constant g_infinity.

Renormalization of charge and spin susceptibilities depends on the wire interaction g.

Threshold structures at rational fillings show effects of the interaction constant g.

Abstract

One-dimensional interacting electrons in a quantum wire connected to reservoirs are studied theoretically. The difference in the Tomonaga-Luttinger interaction constants between the wire (g) and reservoirs $(g_{\infty})$ produces the cross-correlation between the right- and left-going chiral components of the charge density wave field. The low energy asymptotics of this field correlator, which is determined by (g) and $(g_{\infty})$, specifies renormalization of physical quantities. We have found that charge of the carriers in the shot noise is determined by $g_\infty$ (no renormalization for the Fermi liquid reservoirs) at any energy, meanwhile the factor g renormalizing the charge and spin susceptibilities emerges in the threshold structures at some rational fillings.