Bosonization and Scale Invariance on Quantum Wires

TL;DR

This paper develops a comprehensive framework for bosonization and vertex algebras on quantum star graphs, classifies critical points with scale-invariant interactions, and analyzes conductance behavior at these points.

Contribution

It introduces a systematic approach to bosonization on quantum wires, classifies all critical points with scale invariance, and links conductance to Casimir energy in this setting.

Findings

Complete classification of critical points on star graphs.

Explicit bosonization of fermions in the massless Thirring model.

Derived relation between conductance and Casimir energy density.

Abstract

We develop a systematic approach to bosonization and vertex algebras on quantum wires of the form of star graphs. The related bosonic fields propagate freely in the bulk of the graph, but interact at its vertex. Our framework covers all possible interactions preserving unitarity. Special attention is devoted to the scale invariant interactions, which determine the critical properties of the system. Using the associated scattering matrices, we give a complete classification of the critical points on a star graph with any number of edges. Critical points where the system is not invariant under wire permutations are discovered. By means of an appropriate vertex algebra we perform the bosonization of fermions and solve the massless Thirring model. In this context we derive an explicit expression for the conductance and investigate its behavior at the critical points. A simple relation between the conductance and the Casimir energy density is pointed out.