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.
Highlights
Transport properties of the strongly correlated quasi-onedimensional (1D) quantum systems have been the subject of intensive investigation in recent years due to the potential applications in nanoelectronics
In this work we focus on an important class of the quasi-1D transport problem: junctions of multiple Tomonaga-Luttinger liquid (TLL) wires
We have developed a numerical framework to study the transport properties of two-wire junctions with inequivalent TLL wires, based on a finite window embedded in an infinite wire
Summary
Transport properties of the strongly correlated quasi-onedimensional (1D) quantum systems have been the subject of intensive investigation in recent years due to the potential applications in nanoelectronics. [18,42,43] a general method to extract the conductance tensor of the multiwire junction is proposed and is used to study the multiwire junction of equivalent and inequivalent TLLs. By using boundary conformal field theory, the conductance tensor is related to the static correlation function of a semi-infinite system. [56] to calculate the static current-current correlation function of the two-wire junction and use the method proposed in Refs. We note in passing that this provides a consistency check by comparing with results from the time-independent calculations
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