Impurity entropy of junctions of multiple quantum wires

TL;DR

This paper computes the impurity entropy at quantum wire junctions using fermionic perturbation theory and confirms results with boundary conformal field theory and RG flow predictions.

Contribution

It introduces a method to calculate impurity entropy for multi-wire junctions using RPA and verifies it against BCFT and RG flow results.

Findings

Results agree with BCFT predictions of ground state degeneracy.

Method confirms the g-theorem in RG flows.

Provides a consistent approach to impurity entropy in quantum wire junctions.

Abstract

We calculate the zero-temperature impurity entropy of a junction of multiple quantum wires of interacting spinless fermions. Starting from a given single-particle S-matrix representing a fixed point of the renormalization group (RG) flows, we carry out fermionic perturbation theory in the bulk interactions, with the perturbation series summed in the random phase approximation (RPA). The results agree completely with boundary conformal field theory (BCFT) predictions of the ground state degeneracy, and also with known RG flows through the g-theorem.