Tunneling in Quantum Wires: a Boundary Conformal Field Theory Approach

TL;DR

This paper applies boundary conformal field theory to analyze tunneling in quantum wires, aiming to precisely calculate universal properties of critical points in one-dimensional electron systems with interactions.

Contribution

It introduces a new boundary conformal field theory approach to exactly determine critical properties of tunneling in quantum wires, overcoming previous approximation methods.

Findings

Recovered critical properties of stable phases.

Provided a framework for exact calculations of universal fractional transmission.

Addressed challenges from the complex conformal tower structure.

Abstract

Tunneling through a localized barrier in a one-dimensional interacting electron gas has been studied recently using Luttinger liquid techniques. Stable phases with zero or unit transmission occur, as well as critical points with universal fractional transmission whose properties have only been calculated approximately, using a type of ``$\epsilon$-expansion''. It may be possible to calculate the universal properties of these critical points exactly using the recent boundary conformal field theory technique, although difficulties arise from the $\infty$ number of conformal towers in this $c=4$ theory and the absence of any apparent ``fusion'' principle. Here, we formulate the problem efficiently in this new language, and recover the critical properties of the stable phases.