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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 Aug 7, 2026• 0 citations
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Abstract

The files include all simulation codes and data to reproduce the theoretical results in "Impurity quadrupole moments as local probes of flux sectors in the Kitaev spin liquid".
DOI
10.5281/zenodo.21831028

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

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The files include all simulation codes and data to reproduce the theoretical results in "Impurity quadrupole moments as local probes of flux sectors in the Kitaev spin liquid".

•Aug 7, 2026•0 citations

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

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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.

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

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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.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.

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Z2 flux binding to higher-spin impurities in the Kitaev spin liquid

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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.

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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.
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.