Two-wire junction of inequivalent Tomonaga-Luttinger liquids

Abstract

We develop two 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 voltage 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.