$Z_2$ flux binding to higher-spin impurities in the Kitaev spin liquid

TL;DR

This paper explores how higher-spin magnetic impurities affect $Z_2$ fluxes in Kitaev spin liquids, revealing spin-dependent magnetization, flux-sector transitions, and a novel flux-binding mechanism that extends beyond previous impurity models.

Contribution

It demonstrates the impact of spin-$S$ impurities on flux binding and sector transitions in Kitaev spin liquids, introducing a new flux-binding mechanism for higher-spin impurities.

Findings

Impurity magnetization depends on integer/half-integer spin.

Flux-sector transition from bound-flux to zero-flux at low coupling.

Reentrant bound-flux sector for spin-3/2 impurities, stable under magnetic fields.

Abstract

Stabilizing $Z_2$ fluxes in Kitaev spin liquids (KSLs) is crucial for both characterizing candidate materials and identifying Ising anyons. In this study, we investigate the effects of spin-$S$ magnetic impurities embedded in the spin-1/2 KSL. Utilizing exact diagonalization and density matrix renormalization group methods, we examine the impurity magnetization and ground-state flux sector with varying impurity coupling and spin size. Our findings reveal that impurity magnetization exhibits an integer/half-integer spin dependence, which aligns with analytical predictions, and a flux-sector transition from bound-flux to zero-flux occurs at low coupling strengths, independent of the impurity spin. Notably, for spin-3/2 impurities, we observe a reentrant bound-flux sector, which remains stable under magnetic fields. By considering fermionic representations of our spin Hamiltonian, we provide phenomenological explanations for the transitions. Our results suggest a novel way of binding a flux in KSLs, beyond the proposals of vacancies or Kondo impurities.