Generalized Josephson effect with arbitrary periodicity in quantum magnets

TL;DR

This paper uncovers a generalized fractional Josephson effect in quantum magnets, where the periodicity increases with system size, surpassing known effects in superconductors and connecting to phantom helices.

Contribution

It introduces a novel fractional Josephson effect with variable periodicity in spin chains, extending the understanding of topological phenomena in quantum magnets.

Findings

Periodicities grow linearly with system size in certain spin chains.

The effect surpasses known superconducting Josephson periodicities.

Universal energy-phase relation is established.

Abstract

Easy-plane quantum magnets are strikingly similar to superconductors, allowing for spin supercurrent and an effective superconducting phase stemming from their $U(1)$ rotation symmetry around the $z$-axis. We uncover a generalized fractional Josephson effect with a periodicity that increases linearly with system size in one-dimensional spin-$1/2$ chains at selected anisotropies and phase-fixing boundary fields. The effect combines arbitrary integer periodicities in a single system, exceeding the $4\pi $ and $8\pi $ periodicity of superconducting Josephson effects of Majorana zero modes and other exotic quasiparticles. We reveal a universal energy-phase relation and connect the effect to the recently discovered phantom helices.