Chiral fixed point in a junction of critical spin-1 chains

TL;DR

This paper investigates a junction of three critical spin-1 chains, revealing a chiral fixed point that enables tunable spin circulation and hosts fractional excitations, advancing understanding of topological phases in one-dimensional systems.

Contribution

It identifies a chiral fixed point in a junction of critical spin-1 chains described by the SU(2)₂ Wess-Zumino-Witten model, showing its role in spin transport and fractional excitations.

Findings

Discovery of a chiral fixed point at the transition line.

Continuous variation of spin conductance with coupling.

Presence of fractional excitations like Majorana fermions.

Abstract

Junctions of one-dimensional systems are of great interest to the development of synthetic materials that harbor topological phases. We study a junction of three gapless spin-1 chains described by the $\mathrm{SU(2)}_{2}$ Wess-Zumino-Wittten model and coupled by exchange and chiral three-spin interactions. We show that a chiral fixed point appears as a special point on the transition line separating two regimes described by open boundary conditions, corresponding to decoupled chains and the formation of a boundary spin singlet state. Along this transition line, the junction behaves as a tunable spin circulator as the spin conductance varies continuously with the coupling constant of a marginal boundary operator. Since the spectrum of the junction contains fractional excitations such as Majorana fermions, in this paper, we set the stage for network constructions of non-Abelian chiral spin liquids.