Simple approach for the two-terminal conductance through interacting clusters

TL;DR

This paper introduces a new method to calculate two-terminal conductance in interacting clusters by mapping them onto non-interacting systems with renormalized parameters, simplifying the analysis of complex quantum systems.

Contribution

The paper presents a novel approach that transforms an interacting cluster into a non-interacting equivalent, enabling easier computation of conductance in quantum systems.

Findings

Method successfully applied to spinless fermions in an AB2 ring

Interaction effects modify the conductance peak and cause particle number jumps

Provides a systematic way to analyze interacting quantum transport phenomena

Abstract

We present a new method for the determination of the two-terminal differential conductance through an interacting cluster, where one maps the interacting cluster into a non-interacting cluster of $M$ independent sites (where $M$ is the number of cluster states with one particle more or less than the ground state of the cluster), with different onsite energy and connected to the leads with renormalized hoppings constants. The onsite energies are determined from the one-particle (one-hole) excitations of the interacting cluster and the hopping terms are given by the overlap between the interacting $N$ particle ground state and the one-particle (one-hole) excitations of the interacting cluster with $N$-1 ($N$+1) particles. The conductance is obtained from the solution of a system of $M$+2 coupled linear equations. We apply this method to the case of the conductance of spinless fermions through an AB$_2$ ring taking into account nearest neighbors interactions. We discuss the effects of interactions on the zero frequency dipped conductance peak characteristic of the non-interacting AB$_2$ ring as well as the consequences of a particle number jump that occurs as the gate potential is varied.