Dual fermionic variables and renormalization group approach to junctions of strongly interacting quantum wires

TL;DR

This paper introduces a dual fermionic transformation technique that simplifies the analysis of strongly interacting quantum wire junctions, enabling a renormalization group approach to explore phase diagrams and conductance crossovers.

Contribution

It develops a novel dual fermionic framework that extends fermionic RG methods to strongly interacting junctions of quantum wires.

Findings

Mapped the phase diagram of quantum wire junctions.

Mapped conductance tensor crossovers between fixed points.

Provided a dual fermionic approach for strongly interacting systems.

Abstract

Making a combined use of bosonization and fermionization techniques, we build nonlocal transformations between dual fermion operators, describing junctions of strongly interacting spinful one-dimensional quantum wires. Our approach allows for trading strongly interacting (in the original coordinates) fermionic Hamiltonians for weakly interacting (in the dual coordinates) ones. It enables us to generalize to the strongly interacting regime the fermionic renormalization group approach to weakly interacting junctions. As a result, on one hand, we are able to pertinently complement the information about the phase diagram of the junction obtained within bosonization approach; on the other hand, we map out the full crossover of the conductance tensors between any two fixed points in the phase diagram connected by a renormalization group trajectory.