Transport in a class of exactly solvable models of interacting fermions

TL;DR

This paper investigates transport properties in exactly solvable one-dimensional interacting fermion models, revealing how magnetic impurities can effectively cut the wire, unlike non-magnetic impurities unaffected by interactions.

Contribution

It provides an analysis of impurity effects in solvable interacting fermion models, highlighting the different impacts of magnetic and non-magnetic impurities on transport.

Findings

Non-magnetic impurity strength remains unaffected by interactions.

Magnetic impurity effectively cuts the wire at the impurity site.

Interactions do not alter the impurity's effect on non-magnetic impurities.

Abstract

We study transport in a class of exactly solvable models of interacting fermions in one dimension. We contrast these models with models of non-interacting fermions in an Aharanov-Bohm ring to which they are superficially similar. We introduce magnetic and non-magnetic impurities at a site, through either a weak $\delta$-function potential or through a weak link. Using a renormalisation group analysis, we show that the strength of the nonmagnetic impurity is not affected by the interaction, whereas the magnetic impurity cuts the wire at the impurity site.