A conformal field theory description of magnetic flux fractionalization in Josephson junction ladders

TL;DR

This paper applies a conformal field theory framework, specifically the twisted model, to describe flux fractionalization phenomena in Josephson junction ladders, linking topological properties and discrete symmetries.

Contribution

It adapts the twisted model from quantum Hall systems to Josephson junction ladders, elucidating flux fractionalization and topological ground state features.

Findings

Flux fractionalization naturally emerges in the model.

Topological properties relate to half flux quanta.

Discrete symmetries influence the phenomenology.

Abstract

We show how the recently proposed effective theory for a Quantum Hall system at "paired states" filling v=1 (Mod. Phys. Lett. A 15 (2000) 1679; Nucl. Phys. B641 (2002) 547), the twisted model (TM), well adapts to describe the phenomenology of Josephson Junction ladders (JJL) in the presence of defects. In particular it is shown how naturally the phenomenon of flux fractionalization takes place in such a description and its relation with the discrete symmetries present in the TM. Furthermore we focus on closed geometries, which enable us to analyze the topological properties of the ground state of the system in relation to the presence of half flux quanta.