Two-wire Junction of Inequivalent Tomonaga-Luttinger Liquids

TL;DR

This paper introduces two numerical methods using matrix product states to accurately compute the conductance of a junction between two different Tomonaga-Luttinger liquids, confirming analytical predictions.

Contribution

The paper presents two novel numerical schemes for conductance calculation in inequivalent Tomonaga-Luttinger liquids junctions, utilizing matrix product states and finite-size window techniques.

Findings

Excellent agreement with analytical predictions

Effective use of static and dynamic correlation methods

Minimized finite-size effects in conductance calculations

Abstract

We develop two novel numerical schemes to study the conductance of the two-wire junction of inequivalent Tomonaga-Luttinger Liquids. In the first scheme we use the static current-current correlation function across the junction to extract the linear conductance through a relation that is derived via the bosonization method. In the second scheme we apply a bias and evaluate the time-dependent current across the junction to obtain the current-voltage characteristic. The conductance is then extracted from the small bias result within the linear response regime. Both schemes are based on the infinite size matrix product state to minimize the finite-size effects. Due to the lack of the translational invariance, we focus on a finite-size window containing the junction. For time-independent calculations, we use infinite boundary conditions to evaluate the correlations within the window. For time-dependent calculations, we use the window technique to evaluate the local currents within the window. The numerical results obtained by both schemes show excellent agreement with the analytical predictions.