Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2409.02190 · npj Quantum Materials

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

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

Published Jan 29, 2025• 7 citations
arXivHTMLPDF

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.

DOI
10.1038/s41535-025-00729-8

Related papers

Kondo Impurities in the Kitaev Spin Liquid: Numerical Renormalization Group Solution and Gauge-Flux-Driven Screening

Matthias Vojta C, Andrew K. Mitchell, Fabian Zschocke

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.

arXiv:1604.03557•Physical Review Letters•Jul 12, 2016•37 citations

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

Masahiro O. Takahashi, Wen-Han Kao, Satoshi Fujimoto +1 more

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.

arXiv:2603.23145•Mar 24, 2026•0 citations

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

Masahiro O. Takahashi, Wen-Han Kao, Satoshi Fujimoto +1 more

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.

•May 8, 2026•0 citations

Kondo route to spin inhomogeneities in the honeycomb Kitaev model

Shreya Das, Kusum Dhochak, Vikram Tripathi

Paramagnetic impurities in a quantum spin liquid give rise to Kondo effects with highly unusual properties. We have studied the effect of locally coupling a paramagnetic impurity with the spin-$\frac{1}{2}$ honeycomb Kitaev model in its gapless spin-liquid phase. The (impurity) scaling equations are found to be insensitive to the sign of the coupling. The weak and strong coupling fixed points are stable, with the latter corresponding to a noninteracting vacancy and an interacting, spin-1 defect for the antiferromagnetic and ferromagnetic cases, respectively. The ground state in the strong coupling limit in both cases has a nontrivial topology associated with a finite ${Z}_{2}$ flux at the impurity site. For the antiferromagnetic case, this result has been obtained straightforwardly owing to the integrability of the Kitaev model with a vacancy. The strong-coupling limit of the ferromagnetic case is, however, nonintegrable, and we address this problem through exact-diagonalization calculations with finite Kitaev fragments. Our exact diagonalization calculations indicate that the weak-to-strong coupling transition and the topological phase transition occur rather close to each other and are possibly coincident. We also find an intriguing similarity between the magnetic response of the defect and the impurity susceptibility in the two-channel Kondo problem.

arXiv:1509.05721•Physical review. B./Physical review. B•Jul 8, 2016•19 citations

Dynamics of Kitaev spin liquid in a local magnetic field: Emergent Kondo physics and phase transition

Shuang Liang, Bo-Sen He, Zhao-Yang Dong +3 more

We study the dynamics of fractionalized excitations in a Kitaev spin liquid (KSL) induced by a local magnetic field perpendicular to the Kitaev honeycomb lattice. The local magnetic field induces a dynamic excitation of a pair of fluxes described by a generally particle-hole asymmetric interacting resonant level model and the dynamics resembles that of a Kondo problem. The p-h asymmetry competes with the magnetic field and results in a rich phase diagram. Moreover, the magnetic field breaks the gauge equivalence of the ferromagnetic (FM) and anti-ferromagnetic (AFM) Kitaev couplings of the ground state and leads to dramatically different behaviors for the two cases. The latter experiences a first order phase transition during magnetization whereas the former does not. By studying the response of the KSL to the magnetic field in different regimes, we obtain the RG flow and phase diagram of the system in the whole space. This study can be generalized to the KSL in a uniform magnetic field and help resolve issues in recent experiments on KSL candidates.

•Mar 2, 2018•0 citations

Robustness of Vacancy-Bound Non-Abelian Anyons in the Kitaev Model in a Magnetic Field

Bo Xiao, Gonzalo Álvarez, Gábor B. Halász

Non-Abelian anyons in quantum spin liquids (QSLs) provide a promising route to fault-tolerant topological quantum computation. In the exactly solvable Kitaev honeycomb model, such anyons of the QSL state can be bound to nonmagnetic spin vacancies and endowed with non-Abelian statistics by an infinitesimal magnetic field. Here, we investigate how this approach for stabilizing non-Abelian anyons extends to a finite magnetic field represented by a proper Zeeman term. Through large-scale density-matrix renormalization group simulations, we compute the vacancy-anyon binding energy as a function of magnetic field for both the ferromagnetic and antiferromagnetic Kitaev models. We find that anyon binding remains robust within the entire QSL phase for the ferromagnetic Kitaev model but breaks down already inside this phase for the antiferromagnetic Kitaev model. To compute a binding energy several orders of magnitude below the magnetic energy scale, we introduce both a refined definition and an extrapolation scheme based on carefully tailored perturbations.

arXiv:2503.07716•Physical Review Letters•Aug 5, 2025•1 citation
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.
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.
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.
Paramagnetic impurities in a quantum spin liquid give rise to Kondo effects with highly unusual properties. We have studied the effect of locally coupling a paramagnetic impurity with the spin-12\frac{1}{2}21​ honeycomb Kitaev model in its gapless spin-liquid phase. The (impurity) scaling equations are found to be insensitive to the sign of the coupling. The weak and strong coupling fixed points are stable, with the latter corresponding to a noninteracting vacancy and an interacting, spin-1 defect for the antiferromagnetic and ferromagnetic cases, respectively. The ground state in the strong coupling limit in both cases has a nontrivial topology associated with a finite Z2{Z}_{2}Z2​ flux at the impurity site. For the antiferromagnetic case, this result has been obtained straightforwardly owing to the integrability of the Kitaev model with a vacancy. The strong-coupling limit of the ferromagnetic case is, however, nonintegrable, and we address this problem through exact-diagonalization calculations with finite Kitaev fragments. Our exact diagonalization calculations indicate that the weak-to-strong coupling transition and the topological phase transition occur rather close to each other and are possibly coincident. We also find an intriguing similarity between the magnetic response of the defect and the impurity susceptibility in the two-channel Kondo problem.
We study the dynamics of fractionalized excitations in a Kitaev spin liquid (KSL) induced by a local magnetic field perpendicular to the Kitaev honeycomb lattice. The local magnetic field induces a dynamic excitation of a pair of fluxes described by a generally particle-hole asymmetric interacting resonant level model and the dynamics resembles that of a Kondo problem. The p-h asymmetry competes with the magnetic field and results in a rich phase diagram. Moreover, the magnetic field breaks the gauge equivalence of the ferromagnetic (FM) and anti-ferromagnetic (AFM) Kitaev couplings of the ground state and leads to dramatically different behaviors for the two cases. The latter experiences a first order phase transition during magnetization whereas the former does not. By studying the response of the KSL to the magnetic field in different regimes, we obtain the RG flow and phase diagram of the system in the whole space. This study can be generalized to the KSL in a uniform magnetic field and help resolve issues in recent experiments on KSL candidates.
Non-Abelian anyons in quantum spin liquids (QSLs) provide a promising route to fault-tolerant topological quantum computation. In the exactly solvable Kitaev honeycomb model, such anyons of the QSL state can be bound to nonmagnetic spin vacancies and endowed with non-Abelian statistics by an infinitesimal magnetic field. Here, we investigate how this approach for stabilizing non-Abelian anyons extends to a finite magnetic field represented by a proper Zeeman term. Through large-scale density-matrix renormalization group simulations, we compute the vacancy-anyon binding energy as a function of magnetic field for both the ferromagnetic and antiferromagnetic Kitaev models. We find that anyon binding remains robust within the entire QSL phase for the ferromagnetic Kitaev model but breaks down already inside this phase for the antiferromagnetic Kitaev model. To compute a binding energy several orders of magnitude below the magnetic energy scale, we introduce both a refined definition and an extrapolation scheme based on carefully tailored perturbations.