How to find conductance tensors of quantum multi-wire junctions through static calculations: application to an interacting Y-junction

TL;DR

This paper introduces a static calculation method to determine conductance tensors in quantum multi-wire junctions, enabling analysis without time-dependent simulations, and applies it to an interacting Y-junction.

Contribution

It develops a novel static approach to compute conductance tensors, bridging boundary conformal field theory with time-independent numerical methods.

Findings

Verified conductance of the chiral fixed-point in a Y-junction

Computed the unknown conductance of the M fixed point

Demonstrated the method's effectiveness with DMRG simulations

Abstract

Conductance is related to dynamical correlation functions which can be calculated with \textit{time-dependent} methods. Using boundary conformal field theory, we relate the conductance tensors of quantum junctions of multiple wires to static correlation functions in a finite system. We then propose a general method for determining the conductance through \textit{time-independent} calculations alone. Applying the method to a Y-junction of interacting quantum wires, we numerically verify the theoretical prediction for the conductance of the chiral fixed-point of the Y-junction and then calculate the thus far unknown conductance of its M fixed point with time-independent density matrix renormalization group method.