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:1801.03774 · Physical review. B./Physical review. B

Dynamics of a quantum spin liquid beyond integrability: The Kitaev-Heisenberg- Γ model in an augmented parton mean-field theory

Johannes Knolle, Subhro Bhattacharjee, Roderich Moessner

Published Apr 30, 2018• 58 citations
arXivHTMLPDF

Abstract

We present an augmented parton mean-field theory which (i) reproduces the exact ground state, spectrum, and dynamics of the quantum spin-liquid phase of Kitaev's honeycomb model, and (ii) is amenable to the inclusion of integrability breaking terms, allowing a perturbation theory from a controlled starting point. Thus, we exemplarily study dynamical spin correlations of the honeycomb Kitaev quantum spin liquid within the $K\ensuremath{-}J\ensuremath{-}\mathrm{\ensuremath{\Gamma}}$ model, which includes Heisenberg and symmetric-anisotropic (pseudodipolar) interactions. This allows us to trace changes of the correlations in the regime of slowly moving fluxes, where the theory captures the dominant deviations when integrability is lost. These include an asymmetric shift together with a broadening of the dominant peak in the response as a function of frequency, the generation of further-neighbor correlations and their structure in real and spin space, and a resulting loss of an approximate rotational symmetry of the structure factor in reciprocal space. We discuss the limitations of this approach and also view the neutron-scattering experiments on the putative proximate quantum spin-liquid material $\ensuremath{\alpha}\text{\ensuremath{-}}{\mathrm{RuCl}}_{3}$ in the light of the results from this extended parton theory.

DOI
10.1103/physrevb.97.134432

Related papers

Quantum spin liquid signatures in Kitaev-like frustrated magnets

Matthias Gohlke, Gideon Wachtel, Youhei Yamaji +2 more

Motivated by recent experiments on $\ensuremath{\alpha}\ensuremath{-}{\mathrm{RuCl}}_{3}$, we investigate a possible quantum spin liquid ground state of the honeycomb-lattice spin model with bond-dependent interactions. We consider the $K\ensuremath{-}\mathrm{\ensuremath{\Gamma}}$ model, where $K$ and $\mathrm{\ensuremath{\Gamma}}$ represent the Kitaev and symmetric-anisotropic interactions between spin-1/2 moments on the honeycomb lattice. Using the infinite density matrix renormalization group, we provide compelling evidence for the existence of quantum spin liquid phases in an extended region of the phase diagram. In particular, we use transfer-matrix spectra to show the evolution of two-particle excitations with well-defined two-dimensional dispersion, which is a strong signature of a quantum spin liquid. These results are compared with predictions from Majorana mean-field theory and used to infer the quasiparticle excitation spectra. Further, we compute the dynamical structure factor using finite-size cluster computations and show that the results resemble the scattering continuum seen in neutron-scattering experiments on $\ensuremath{\alpha}\ensuremath{-}{\mathrm{RuCl}}_{3}$. We discuss these results in light of recent and future experiments.

arXiv:1706.09908•Physical review. B./Physical review. B•Feb 13, 2018•128 citations

Dynamics and stability of U(1) spin liquids beyond mean-field theory: Triangular-lattice $J_1$-$J_2$ Heisenberg model

Josef Willsher, Johannes Knolle

Quantum spin liquids (QSLs) are long-range entangled phases of frustrated magnets exhibiting fractionalised spin excitations. In two dimensions, there is limited analytical understanding of their excitation spectra beyond parton mean-field theories, which fail to capture many features of the finite frequency dynamical response. We use a self-consistent mean-field theory combined with the random phase approximation (RPA) for the $J_1$-$J_2$ Heisenberg model on the triangular lattice to describe the strong spinon-spinon interactions of the U(1) Dirac QSL. We obtain quantitative results for the dynamical spin structure factor and phase diagram compatible with comprehensive numerical efforts. We show the continuum response at the Brillouin zone corners is described by a spinon-exciton hybridised with monopole gauge excitations. We further show that the transition from the QSL to 120-degree coplanar order is in the QED$_3$ O(3)-GN universality class. We extend the method to chiral QSLs and XXZ anisotropy, and discuss its broad range of applicability to other models and for describing inelastic neutron scattering experiments in KYbSe$_2$.

arXiv:2503.13831•Mar 18, 2025•0 citations

Phase diagram and spin correlations of the Kitaev-Heisenberg model: Importance of quantum effects

Dorota Gotfryd, Juraj Rusnačko, Krzysztof Wohlfeld +3 more

We explore the phase diagram of the Kitaev-Heisenberg model with nearest neighbor interactions on the honeycomb lattice using the exact diagonalization of finite systems combined with the cluster mean field approximation, and supplemented by the insights from analytic approaches: the linear spin-wave and second-order perturbation theories. This study confirms that by varying the balance between the Heisenberg and Kitaev term, frustrated exchange interactions stabilize in this model either one of four phases with magnetic long range order: N\'eel phase, ferromagnetic phase, and two other phases with coexisting antiferromagnetic and ferromagnetic bonds, zigzag and stripy phase, or one of two distinct spin-liquid phases. Out of these latter disordered phases, the one with ferromagnetic Kitaev interactions has a substantially broader range of stability as the neighboring competing ordered phases, ferromagnetic and stripy, have very weak quantum fluctuations. Focusing on the quantum spin-liquid phases, we study spatial spin correlations and dynamic spin structure factor of the model by the exact diagonalization technique, and discuss the evolution of gapped low-energy spin response across the quantum phase transitions between the disordered spin liquid and phases with long range magnetic order.

arXiv:1608.05333•Physical review. B./Physical review. B•Jan 23, 2017•75 citations

Low-Energy Spin Dynamics of the Honeycomb Spin Liquid Beyond the Kitaev Limit

Xue-Yang Song, Yi‐Zhuang You, Leon Balents

We investigate the generic features of the low energy dynamical spin structure factor of the Kitaev honeycomb quantum spin liquid perturbed away from its exact soluble limit by generic symmetry-allowed exchange couplings. We find that the spin gap persists in the Kitaev-Heisenberg model, but generally vanishes provided more generic symmetry-allowed interactions exist. We formulate the generic expansion of the spin operator in terms of fractionalized Majorana fermion operators according to the symmetry enriched topological order of the Kitaev spin liquid, described by its projective symmetry group. The dynamical spin structure factor displays power-law scaling bounded by Dirac cones in the vicinity of the Γ, K, and K^{'} points of the Brillouin zone, rather than the spin gap found for the exactly soluble point.

arXiv:1604.04365•Physical Review Letters•Jul 15, 2016•119 citations

Temperature evolution of spin dynamics in extended Kitaev models within an Abrikosov fermion theory beyond mean field

Daiki Sasamoto, Joji Nasu

The $S=1/2$ Kitaev model provides an exactly solvable setting in which spin fractionalization produces itinerant Majorana fermions coupled to an emergent $\mathbb{Z}_2$ gauge field. In realistic Kitaev magnets, however, non-Kitaev interactions break integrability and make their finite-temperature dynamics difficult to calculate. We develop a finite-temperature parton mean-field theory based on the Abrikosov-fermion representation and incorporate the effects of exchange interactions through the random phase approximation to calculate the dynamical spin structure factor. For the pure Kitaev model, the method reproduces a strong, nearly dispersionless peak at a finite low energy together with a broad continuum at higher energies. It also reproduces the momentum dependence of the dynamical spin structure factor and its temperature evolution, including the downward shift of the low-energy spectral weight, in qualitative agreement with continuous-time quantum Monte Carlo calculations. Within the present theory, the contraction of the continuum is traced to the temperature-induced reduction of the bond amplitudes, which narrows the parton bands and compresses the two-parton phase space. For ferromagnetic Kitaev coupling, the energy of the low-energy peak is minimized at the $Γ$ point for a ferromagnetic Heisenberg interaction and maximized there for an antiferromagnetic interaction. In the ferromagnetic Kitaev-$Γ$ model, the static response develops a finite-momentum softening, indicating an instability toward the period-three magnetic order reported in numerical studies. For uniform-ferromagnetic states selected by a $[111]$ magnetic field, we find that a broad parton continuum coexists with magnonlike dispersive structures, producing spectral features consistent with a spinon-to-magnon crossover.

arXiv:2610.13401•Oct 9, 2026•0 citations

Unveiling the S=3/2 Kitaev honeycomb spin liquids

Hui-Ke Jin, W. M. H. Natori, Frank Pollmann +1 more

Abstract The S=3/2 Kitaev honeycomb model (KHM) is a quantum spin liquid (QSL) state coupled to a static Z2 gauge field. Employing an SO(6) Majorana representation of spin3/2’s, we find an exact representation of the conserved plaquette fluxes in terms of static Z2 gauge fields akin to the S=1/2 KHM which enables us to treat the remaining interacting matter fermion sector in a parton mean-field theory. We uncover a ground-state phase diagram consisting of gapped and gapless QSLs. Our parton description is in quantitative agreement with numerical simulations, and is furthermore corroborated by the addition of a [001] single ion anisotropy (SIA) which continuously connects the gapless Dirac QSL of our model with that of the S=1/2 KHM. In the presence of a weak [111] SIA, we discuss an emergent chiral QSL within a perturbation theory.

arXiv:2107.13364•Nature Communications•Jul 2, 2022•43 citations
We present an augmented parton mean-field theory which (i) reproduces the exact ground state, spectrum, and dynamics of the quantum spin-liquid phase of Kitaev's honeycomb model, and (ii) is amenable to the inclusion of integrability breaking terms, allowing a perturbation theory from a controlled starting point. Thus, we exemplarily study dynamical spin correlations of the honeycomb Kitaev quantum spin liquid within the K\ensuremath−J\ensuremath−\ensuremathΓK\ensuremath{-}J\ensuremath{-}\mathrm{\ensuremath{\Gamma}}K\ensuremath−J\ensuremath−\ensuremathΓ model, which includes Heisenberg and symmetric-anisotropic (pseudodipolar) interactions. This allows us to trace changes of the correlations in the regime of slowly moving fluxes, where the theory captures the dominant deviations when integrability is lost. These include an asymmetric shift together with a broadening of the dominant peak in the response as a function of frequency, the generation of further-neighbor correlations and their structure in real and spin space, and a resulting loss of an approximate rotational symmetry of the structure factor in reciprocal space. We discuss the limitations of this approach and also view the neutron-scattering experiments on the putative proximate quantum spin-liquid material \ensuremathα\ensuremath-RuCl3\ensuremath{\alpha}\text{\ensuremath{-}}{\mathrm{RuCl}}_{3}\ensuremathα\ensuremath-RuCl3​ in the light of the results from this extended parton theory.
Motivated by recent experiments on $\ensuremath{\alpha}\ensuremath{-}{\mathrm{RuCl}}_{3}$, we investigate a possible quantum spin liquid ground state of the honeycomb-lattice spin model with bond-dependent interactions. We consider the $K\ensuremath{-}\mathrm{\ensuremath{\Gamma}}$ model, where KKK and $\mathrm{\ensuremath{\Gamma}}$ represent the Kitaev and symmetric-anisotropic interactions between spin-1/2 moments on the honeycomb lattice. Using the infinite density matrix renormalization group, we provide compelling evidence for the existence of quantum spin liquid phases in an extended region of the phase diagram. In particular, we use transfer-matrix spectra to show the evolution of two-particle excitations with well-defined two-dimensional dispersion, which is a strong signature of a quantum spin liquid. These results are compared with predictions from Majorana mean-field theory and used to infer the quasiparticle excitation spectra. Further, we compute the dynamical structure factor using finite-size cluster computations and show that the results resemble the scattering continuum seen in neutron-scattering experiments on $\ensuremath{\alpha}\ensuremath{-}{\mathrm{RuCl}}_{3}$. We discuss these results in light of recent and future experiments.
Dynamics and stability of U(1) spin liquids beyond mean-field theory: Triangular-lattice J1J_1J1​-J2J_2J2​ Heisenberg model
Quantum spin liquids (QSLs) are long-range entangled phases of frustrated magnets exhibiting fractionalised spin excitations. In two dimensions, there is limited analytical understanding of their excitation spectra beyond parton mean-field theories, which fail to capture many features of the finite frequency dynamical response. We use a self-consistent mean-field theory combined with the random phase approximation (RPA) for the J1J_1J1​-J2J_2J2​ Heisenberg model on the triangular lattice to describe the strong spinon-spinon interactions of the U(1) Dirac QSL. We obtain quantitative results for the dynamical spin structure factor and phase diagram compatible with comprehensive numerical efforts. We show the continuum response at the Brillouin zone corners is described by a spinon-exciton hybridised with monopole gauge excitations. We further show that the transition from the QSL to 120-degree coplanar order is in the QED3_33​ O(3)-GN universality class. We extend the method to chiral QSLs and XXZ anisotropy, and discuss its broad range of applicability to other models and for describing inelastic neutron scattering experiments in KYbSe2_22​.
We explore the phase diagram of the Kitaev-Heisenberg model with nearest neighbor interactions on the honeycomb lattice using the exact diagonalization of finite systems combined with the cluster mean field approximation, and supplemented by the insights from analytic approaches: the linear spin-wave and second-order perturbation theories. This study confirms that by varying the balance between the Heisenberg and Kitaev term, frustrated exchange interactions stabilize in this model either one of four phases with magnetic long range order: N\'eel phase, ferromagnetic phase, and two other phases with coexisting antiferromagnetic and ferromagnetic bonds, zigzag and stripy phase, or one of two distinct spin-liquid phases. Out of these latter disordered phases, the one with ferromagnetic Kitaev interactions has a substantially broader range of stability as the neighboring competing ordered phases, ferromagnetic and stripy, have very weak quantum fluctuations. Focusing on the quantum spin-liquid phases, we study spatial spin correlations and dynamic spin structure factor of the model by the exact diagonalization technique, and discuss the evolution of gapped low-energy spin response across the quantum phase transitions between the disordered spin liquid and phases with long range magnetic order.
We investigate the generic features of the low energy dynamical spin structure factor of the Kitaev honeycomb quantum spin liquid perturbed away from its exact soluble limit by generic symmetry-allowed exchange couplings. We find that the spin gap persists in the Kitaev-Heisenberg model, but generally vanishes provided more generic symmetry-allowed interactions exist. We formulate the generic expansion of the spin operator in terms of fractionalized Majorana fermion operators according to the symmetry enriched topological order of the Kitaev spin liquid, described by its projective symmetry group. The dynamical spin structure factor displays power-law scaling bounded by Dirac cones in the vicinity of the Γ, K, and K^{'} points of the Brillouin zone, rather than the spin gap found for the exactly soluble point.
The S=1/2S=1/2S=1/2 Kitaev model provides an exactly solvable setting in which spin fractionalization produces itinerant Majorana fermions coupled to an emergent Z2\mathbb{Z}_2Z2​ gauge field. In realistic Kitaev magnets, however, non-Kitaev interactions break integrability and make their finite-temperature dynamics difficult to calculate. We develop a finite-temperature parton mean-field theory based on the Abrikosov-fermion representation and incorporate the effects of exchange interactions through the random phase approximation to calculate the dynamical spin structure factor. For the pure Kitaev model, the method reproduces a strong, nearly dispersionless peak at a finite low energy together with a broad continuum at higher energies. It also reproduces the momentum dependence of the dynamical spin structure factor and its temperature evolution, including the downward shift of the low-energy spectral weight, in qualitative agreement with continuous-time quantum Monte Carlo calculations. Within the present theory, the contraction of the continuum is traced to the temperature-induced reduction of the bond amplitudes, which narrows the parton bands and compresses the two-parton phase space. For ferromagnetic Kitaev coupling, the energy of the low-energy peak is minimized at the ΓΓΓ point for a ferromagnetic Heisenberg interaction and maximized there for an antiferromagnetic interaction. In the ferromagnetic Kitaev-ΓΓΓ model, the static response develops a finite-momentum softening, indicating an instability toward the period-three magnetic order reported in numerical studies. For uniform-ferromagnetic states selected by a [111][111][111] magnetic field, we find that a broad parton continuum coexists with magnonlike dispersive structures, producing spectral features consistent with a spinon-to-magnon crossover.
Abstract The S=3/2 Kitaev honeycomb model (KHM) is a quantum spin liquid (QSL) state coupled to a static Z2 gauge field. Employing an SO(6) Majorana representation of spin3/2’s, we find an exact representation of the conserved plaquette fluxes in terms of static Z2 gauge fields akin to the S=1/2 KHM which enables us to treat the remaining interacting matter fermion sector in a parton mean-field theory. We uncover a ground-state phase diagram consisting of gapped and gapless QSLs. Our parton description is in quantitative agreement with numerical simulations, and is furthermore corroborated by the addition of a [001] single ion anisotropy (SIA) which continuously connects the gapless Dirac QSL of our model with that of the S=1/2 KHM. In the presence of a weak [111] SIA, we discuss an emergent chiral QSL within a perturbation theory.