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arXiv:2603.23145

Impurity quadrupole moments as local probes of flux sectors in the Kitaev spin liquid

Masahiro O. Takahashi, Wen-Han Kao, Satoshi Fujimoto, Natalia Borisovna Perkins

Published Mar 24, 2026• 0 citations
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Abstract

Emergent fluxes play a central role in the low-energy properties of quantum spin liquids (QSLs), where they encode the underlying gauge structure and fractionalization of spins. Here, we show that the quadrupole moment of magnetic impurities provides a direct probe of these flux configurations in QSLs and can be measured by local tunneling spectroscopy. Employing the SO(6) Majorana representation for spin-3/2 impurity operators in the isotropic Kitaev spin liquid together with a self-consistent mean-field approximation for impurity-related terms, we show that the ground-state flux sector can be identified by discontinuous jumps of the impurity quadrupole moment at the flux sector transition points. We also demonstrate that the quadrupole correlations between impurities under a magnetic field exhibit exponential decay, with decay rates that depend sensitively on the flux sector. Furthermore, we discuss the stability of pi fluxes bound to impurities with respect to model parameters and internal flux configurations, and relate our findings to Lieb's conjecture on flux configurations. These results establish the quadrupole moments of magnetic impurities as a sensitive tool to study fractionalized excitations and flux physics in Kitaev magnets.

DOI
10.48550/arxiv.2603.23145

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Emergent fluxes play a central role in the low-energy properties of quantum spin liquids (QSLs), where they encode the underlying gauge structure and fractionalization of spins. Here, we show that the quadrupole moment of magnetic impurities provides a direct probe of these flux configurations in QSLs and can be measured by local tunneling spectroscopy. Employing the SO(6) Majorana representation for spin-3/2 impurity operators in the isotropic Kitaev spin liquid together with a self-consistent mean-field approximation for impurity-related terms, we show that the ground-state flux sector can be identified by discontinuous jumps of the impurity quadrupole moment at the flux sector transition points. We also demonstrate that the quadrupole correlations between impurities under a magnetic field exhibit exponential decay, with decay rates that depend sensitively on the flux sector. Furthermore, we discuss the stability of pi fluxes bound to impurities with respect to model parameters and internal flux configurations, and relate our findings to Lieb's conjecture on flux configurations. These results establish the quadrupole moments of magnetic impurities as a sensitive tool to study fractionalized excitations and flux physics in Kitaev magnets.
Abstract Emergent fluxes play a central role in the low-energy properties of quantum spin liquids (QSLs),where they encode the underlying gauge structure and fractionalization of spins.Here, we show that the quadrupole moment of magnetic impurities provides a direct probe of these flux configurations in QSLs.Employing the SO(6) Majorana representation for spin-3/2 impurity operators in the isotropic Kitaev spin liquid together with a self-consistent mean-field approximation for impurity-related terms, we show that the ground-state flux sector can be identified by discontinuous jumps of the impurity quadrupole moment at the flux sector transition points.We also demonstrate that the quadrupole correlations between impurities under a magnetic field exhibit exponential decay, with decay rates that depend sensitively on the flux sector.Furthermore, we discuss the stability of π\piπ-fluxes bound to impurities with respect to model parameters and internal flux configurations, and relate our findings to Lieb’s conjecture on flux configurations.These results establish the quadrupole moments of magnetic impurities as a sensitive tool to study fractionalized excitations and flux physics in Kitaev magnets.
Kitaev's honeycomb-lattice compass model describes a spin liquid with emergent fractionalized excitations. Here, we study the physics of isolated magnetic impurities coupled to the Kitaev spin-liquid host. We reformulate this Kondo-type problem in terms of a many-state quantum impurity coupled to a multichannel bath of Majorana fermions and present the numerically exact solution using Wilson's numerical renormalization group technique. Quantum phase transitions occur as a function of Kondo coupling and locally applied field. At zero field, the impurity moment is partially screened only when it binds an emergent gauge flux, while otherwise it becomes free at low temperatures. We show how Majorana degrees of freedom determine the fixed-point properties, make contact with Kondo screening in pseudogap Fermi systems, and discuss effects away from the dilute limit.
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.
Quantum spin liquids (QSLs) host a variety of fractionalized particles. In Kitaev's paradigmatic honeycomb model a spin-fractionalizes intoflux due to emergentgauge field and matter Majorana fermions. Although these excitations have well-defined dynamics in the integrable limit, their direct experimental identification is notoriously challenging: realistic materials inevitably host additional symmetry-allowed interactions that break integrability and hybridize gauge and matter sectors, while magnetic fields, which are often required to suppress competing order and stabilize a putative QSL regime, further entangle the responses of different fractionalized quasiparticles and may even drive the system into field-induced spin-liquid phases that are not adiabatically connected to the integrable limit. A prominent example is the quantum Majorana metal, in which the distinct dynamics of fractionalized Majorana fermions can become directly visible in scattering. This review highlights recent progress on these related questions: in which field-stabilized QSL regimes and nearby emergent phases, and under what conditions, can the response of a specific fractionalized quasiparticle be isolated and positively understood, thereby clarifying the existence and the experimental scope of putative spin liquids? We review the progress on these questions across Abelian, non-Abelian, and emergent quantum phases under magnetic field that are not perturbatively connected to the integrable limit. We connect these field-induced dynamical phenomena to concrete experimental observables, relevant for neutron scattering, resonant inelastic x-ray scattering, and pump-probe spectroscopy, techniques that are capable of identifying the nature of different magnetic-field-induced phases and resolving specific types of fractionalized particles, including Majoranas andfluxes.