A fermionic approach to tunneling through junctions of multiple quantum wires

摘要

Junctions of multiple one-dimensional quantum wires of interacting electronshave received considerable theoretical attention as a basic constituent ofquantum circuits. While results have been obtained on these models usingbosonization and Density Matrix Renormalization Group (DMRG) methods, anotherpowerful technique is based on direct perturbation theory in the bulkinteractions, combined with the Renormalization Group (RG) and summed in theRandom Phase Approximation (RPA). This technique has so far only been appliedto the case where finite length interacting wires are attached tonon-interacting Fermi liquid leads. We reformulate it in terms of thesingle-particle S-matrix, formally unifying treatments of junctions ofdifferent numbers of leads, and extend this method to cover the case ofinfinite length interacting leads obtaining results on 2-lead and 3-leadjunctions in good agreement with previous bosonization and DMRG results.