General method for calculating the universal conductance of strongly correlated junctions of multiple quantum wires

TL;DR

This paper introduces a novel static ground-state computational method, based on boundary conformal field theory, to accurately determine the universal conductance of strongly correlated quantum wire junctions, facilitating studies of quantum transport with electron interactions.

Contribution

It presents a systematic, efficient approach to compute conductance from ground-state correlations, applicable to strongly interacting systems, using standard numerical techniques like DMRG.

Findings

Validated the method through tests and benchmarks.

Calculated conductance for the Y junction of Luttinger liquids.

Conjectured the functional dependence of conductance on the Luttinger parameter.

Abstract

We develop a method to extract the universal conductance of junctions of multiple quantum wires, a property of systems connected to reservoirs, from static ground-state computations in closed finite systems. The method is based on a key relationship, derived within the framework of boundary conformal field theory, between the conductance tensor and certain ground state correlation functions. Our results provide a systematic way of studying quantum transport in the presence of strong electron-electron interactions using efficient numerical techniques such as the standard time-independent density-matrix renormalization-group method. We give a step-by-step recipe for applying the method and present several tests and benchmarks. As an application of the method, we calculate the conductance of the M fixed point of a Y junction of Luttinger liquids for several values of the Luttinger parameter $g$ and conjecture its functional dependence on $g$.