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:2206.08946

Tangle of Spin Double Helices in the Honeycomb Kitaev-ΓΓΓ Model

Jheng-Wei Li, Rao, Nihal, Jan von Delft, Lode Pollet, Ke Liu

Published Jun 17, 2022• 2 citations
arXivHTMLPDF

Abstract

We investigate the ground-state nature of the honeycomb Kitaev-$Γ$ model in the material-relevant parameter regime through a combination of classical and quantum simulations. The classical model is imprinted with a tangle of highly structured spin double helices. This helix tangle exhibits $18$ inequivalent helical axes and features a spontaneous periodicity anisotropy and a ${\rm sgn}(Γ)$-determined chirality pattern. Infinite PEPS simulations with clusters up to $36$ sites identify hallmarks of this many-body order in the quantum spin-$1/2$ model. Our findings provide a fresh perspective of the Kitaev-$Γ$ model and enrich the physics of Kitaev magnetism.

DOI
10.48550/arxiv.2206.08946

Related papers

Tangle of spin double helices in the honeycomb Kitaev- Γ model

Jheng-Wei Li, Nihal Rao, Jan von Delft +2 more

We investigate the ground-state nature of the honeycomb Kitaev- Γ model in the material-relevant parameter regime through a combination of analytics and classical and quantum simulations. We find the classical model is imprinted with a tangle of highly structured spin double helices. This helix tangle consists of 18 inequivalent helices and features modulation of multiple rotation axes, an anisotropy in spacial periodicities indicative of spontaneous symmetry breaking, and a sgn ( Γ ) -determined chirality pattern. Infinite projected entangled pair state simulations with clusters of up to 36 sites identify hallmarks of this unprecedented many-body order in the quantum spin- 1 / 2 model. Our findings provide a fresh perspective of the Kitaev- Γ model and enrich the physics of the Kitaev magnetism.

Physical review. B./Physical review. B•Jan 21, 2026•1 citation

Kitaev honeycomb antiferromagnet in a field: quantum phase diagram for general spin

Saeed S. Jahromi, Max Hörmann, Patrick Adelhardt +4 more

We use tensor-network methods and high-order linked-cluster expansions to explore the quantum phase diagram of the antiferromagnetic Kitaev honeycomb model in a magnetic field for general spin S values. Tensor network calculations for the pure Kitaev model confirm the absence of fluxes and spin-spin correlations beyond nearest neighbors, while revealing discrete orientational symmetry breaking for S ∈ 1, 3/2, 2, consistent with the semiclassical limit. An intermediate region between Kitaev phases and the high-field polarized phase is identified for all considered spin values, showing a sequence of potential phases characterized by distinct local magnetization patterns while the total magnetization increases smoothly as a function of the field. Linked-cluster expansions for the high-field zero-momentum gap and spectral weight indicate a quantum critical breakdown of the polarized phase, suggesting exotic physics at intermediate Kitaev couplings. The antiferromagnetic spin 1/2 Kitaev model is known to have an intermediate phase under a magnetic field before transitioning to a fully polarized state. However, the nature of this phase for higher spins remained unclear. This paper explores the quantum phase diagram of the antiferromagnetic Kitaev honeycomb model in a magnetic field using tensor-network methods and high-order linked cluster expansions, uncovering an intermediate phase with distinct local magnetization patterns across different spin values.

arXiv:2111.06132•Communications Physics•Oct 4, 2024•8 citations

Ferrimagnetic Kitaev spin liquids in mixed spin- 1 2 and spin- 3 2 honeycomb magnets

W. M. H. Natori, Yang Yang, Hui-Ke Jin +2 more

We explore the phase diagram of a mixed-spin Kitaev model, where spin-1/2 and spin-3/2 ions form a staggered pattern on a honeycomb lattice. Enabled by an exact mapping of local conserved flux operators onto ${Z}_{2}$ gauge fields, we perform a parton mean-field theory for the model with a single-ion anisotropy. The phase diagram contains four types of quantum spin liquids distinguished by quadrupolar parameters. These analytical results are quantitatively confirmed by state-of-the-art DMRG simulations. We also explore the potential experimental realization of the mixed-spin Kitaev model in materials such as ${\mathrm{Zr}}_{0.5}{\mathrm{Ru}}_{0.5}{\mathrm{Cl}}_{3}$. By developing a superexchange theory specifically for this mixed-spin system, we identify the conditions under which dominant Kitaev-like interactions emerge. Our findings highlight the importance of spin-orbital couplings and quadrupolar order parameters in stabilizing exotic phases, providing a foundation for exploring mixed-spin Kitaev magnets.

Physical review. B./Physical review. B•Jun 4, 2025•1 citation

Fractional excitations in Kitaev quasi-one-dimensional chain

Ritwika Majumder

The Kitaev honeycomb model has attracted significant interest due to its quantum spin liquid ground state, fractionalized Majorana excitations, and topological properties. Motivated by these features, we introduce a quasi-one-dimensional Kitaev-like spin chain derived from a truncated honeycomb geometry. The resulting Majorana band structure contains both dispersive and flat bands, with a gap closing at a critical anisotropy that separates trivial and chiral topological phases. Under open boundary conditions, the topological regime hosts zero-energy edge modes protected by chiral symmetry, placing the system in the BDI symmetry class with a quantized winding number. In the excited spectrum, localized plaquette modes emerge near zero energy and can be tuned by introducing domains of negative plaquettes. The dynamical spin correlation function reveals broad continua associated with fractionalized excitations, together with characteristic low-energy spectral weight from edge Majorana modes. These features distinguish the present system from conventional Heisenberg spin chains and provide experimentally relevant fingerprints of chiral topological order. Our model thus establishes a conceptual bridge between the two-dimensional Kitaev spin liquid and Kitaev's one-dimensional quantum wire.

arXiv:2606.20309•Jun 18, 2026•0 citations

Ferrimagnetic Kitaev spin liquids in mixed spin 1/2 spin 3/2 honeycomb magnets

W. M. H. Natori, Yang Yang, Hui-Ke Jin +2 more

We explore the potential experimental realization of the mixed-spin Kitaev model in materials such as Zr$_{0.5}$Ru$_{0.5}$Cl$_3$, where spin-1/2 and spin-3/2 ions occupy distinct sublattices of a honeycomb lattice. By developing a superexchange theory specifically for this mixed-spin system, we identify the conditions under which dominant Kitaev-like interactions emerge. Focusing on the limiting case of pure Kitaev coupling with single-ion anisotropy, we employ a combination of superexchange theory, parton mean-field theory, and density matrix renormalization group (DMRG) simulations. We establish a comprehensive ground-state phase diagram identifying four distinct quantum spin liquid phases. Our findings highlight the importance of spin-orbital couplings and quadrupolar order parameters in stabilizing exotic phases, providing a foundation for exploring mixed-spin Kitaev magnets.

arXiv:2412.09310•Dec 12, 2024•0 citations

Phase transitions in the classical exchange-anisotropic Kitaev-Heisenberg model

X. M. Zhang, R. M. Liu, Zuanming Jin +8 more

The Kitaev model on the honeycomb lattice has been receiving substantial attention due to the discovery of quantum spin liquid state associated with this model. Consequently, its classical partners such as the Kitaev-Heisenberg (KH) model and associated phase transitions become concerned. Specifically, an intermediate Kosterlitz-Thouless (KT) phase engaged in the transition from the high-temperature (T) disordered state to the low-T sixfold degenerate state is predicted in the isotropic KH model [Phys. Rev. Lett. 109, 187201 (2012)10.1103/PhysRevLett.109.187201], but so far no sufficient experimental proof has been reported. In this work, we consider an essential extension of this KH model on the honeycomb lattice by including the Kitaev exchange anisotropy that is non-negligible in realistic materials. The associated phase transitions are thus investigated using the Monte Carlo simulations. It is found that such an anisotropy will result in a degradation of the sixfold degeneracy of the ground state in the isotropic KH model down to the fourfold or twofold degenerate ground state, and the finite-T phase transitions will also be modified remarkably. Interestingly, the intermediate KT phase can be suppressed by this Kitaev exchange anisotropy. This work thus provides a more realistic description of the physics ingredient with the KH model and presents a possible explanation on absence of the intermediate phase in real materials where the Kitaev exchange anisotropy can be more or less available.

Physical review. E•Oct 27, 2020•3 citations
We investigate the ground-state nature of the honeycomb Kitaev-ΓΓΓ model in the material-relevant parameter regime through a combination of classical and quantum simulations. The classical model is imprinted with a tangle of highly structured spin double helices. This helix tangle exhibits 181818 inequivalent helical axes and features a spontaneous periodicity anisotropy and a sgn(Γ){\rm sgn}(Γ)sgn(Γ)-determined chirality pattern. Infinite PEPS simulations with clusters up to 363636 sites identify hallmarks of this many-body order in the quantum spin-1/21/21/2 model. Our findings provide a fresh perspective of the Kitaev-ΓΓΓ model and enrich the physics of Kitaev magnetism.
We investigate the ground-state nature of the honeycomb Kitaev- Γ model in the material-relevant parameter regime through a combination of analytics and classical and quantum simulations. We find the classical model is imprinted with a tangle of highly structured spin double helices. This helix tangle consists of 18 inequivalent helices and features modulation of multiple rotation axes, an anisotropy in spacial periodicities indicative of spontaneous symmetry breaking, and a sgn ( Γ ) -determined chirality pattern. Infinite projected entangled pair state simulations with clusters of up to 36 sites identify hallmarks of this unprecedented many-body order in the quantum spin- 1 / 2 model. Our findings provide a fresh perspective of the Kitaev- Γ model and enrich the physics of the Kitaev magnetism.
We use tensor-network methods and high-order linked-cluster expansions to explore the quantum phase diagram of the antiferromagnetic Kitaev honeycomb model in a magnetic field for general spin S values. Tensor network calculations for the pure Kitaev model confirm the absence of fluxes and spin-spin correlations beyond nearest neighbors, while revealing discrete orientational symmetry breaking for S ∈ 1, 3/2, 2, consistent with the semiclassical limit. An intermediate region between Kitaev phases and the high-field polarized phase is identified for all considered spin values, showing a sequence of potential phases characterized by distinct local magnetization patterns while the total magnetization increases smoothly as a function of the field. Linked-cluster expansions for the high-field zero-momentum gap and spectral weight indicate a quantum critical breakdown of the polarized phase, suggesting exotic physics at intermediate Kitaev couplings. The antiferromagnetic spin 1/2 Kitaev model is known to have an intermediate phase under a magnetic field before transitioning to a fully polarized state. However, the nature of this phase for higher spins remained unclear. This paper explores the quantum phase diagram of the antiferromagnetic Kitaev honeycomb model in a magnetic field using tensor-network methods and high-order linked cluster expansions, uncovering an intermediate phase with distinct local magnetization patterns across different spin values.
We explore the phase diagram of a mixed-spin Kitaev model, where spin-1/2 and spin-3/2 ions form a staggered pattern on a honeycomb lattice. Enabled by an exact mapping of local conserved flux operators onto Z2{Z}_{2}Z2​ gauge fields, we perform a parton mean-field theory for the model with a single-ion anisotropy. The phase diagram contains four types of quantum spin liquids distinguished by quadrupolar parameters. These analytical results are quantitatively confirmed by state-of-the-art DMRG simulations. We also explore the potential experimental realization of the mixed-spin Kitaev model in materials such as Zr0.5Ru0.5Cl3{\mathrm{Zr}}_{0.5}{\mathrm{Ru}}_{0.5}{\mathrm{Cl}}_{3}Zr0.5​Ru0.5​Cl3​. By developing a superexchange theory specifically for this mixed-spin system, we identify the conditions under which dominant Kitaev-like interactions emerge. Our findings highlight the importance of spin-orbital couplings and quadrupolar order parameters in stabilizing exotic phases, providing a foundation for exploring mixed-spin Kitaev magnets.
The Kitaev honeycomb model has attracted significant interest due to its quantum spin liquid ground state, fractionalized Majorana excitations, and topological properties. Motivated by these features, we introduce a quasi-one-dimensional Kitaev-like spin chain derived from a truncated honeycomb geometry. The resulting Majorana band structure contains both dispersive and flat bands, with a gap closing at a critical anisotropy that separates trivial and chiral topological phases. Under open boundary conditions, the topological regime hosts zero-energy edge modes protected by chiral symmetry, placing the system in the BDI symmetry class with a quantized winding number. In the excited spectrum, localized plaquette modes emerge near zero energy and can be tuned by introducing domains of negative plaquettes. The dynamical spin correlation function reveals broad continua associated with fractionalized excitations, together with characteristic low-energy spectral weight from edge Majorana modes. These features distinguish the present system from conventional Heisenberg spin chains and provide experimentally relevant fingerprints of chiral topological order. Our model thus establishes a conceptual bridge between the two-dimensional Kitaev spin liquid and Kitaev's one-dimensional quantum wire.
We explore the potential experimental realization of the mixed-spin Kitaev model in materials such as Zr0.5_{0.5}0.5​Ru0.5_{0.5}0.5​Cl3_33​, where spin-1/2 and spin-3/2 ions occupy distinct sublattices of a honeycomb lattice. By developing a superexchange theory specifically for this mixed-spin system, we identify the conditions under which dominant Kitaev-like interactions emerge. Focusing on the limiting case of pure Kitaev coupling with single-ion anisotropy, we employ a combination of superexchange theory, parton mean-field theory, and density matrix renormalization group (DMRG) simulations. We establish a comprehensive ground-state phase diagram identifying four distinct quantum spin liquid phases. Our findings highlight the importance of spin-orbital couplings and quadrupolar order parameters in stabilizing exotic phases, providing a foundation for exploring mixed-spin Kitaev magnets.
The Kitaev model on the honeycomb lattice has been receiving substantial attention due to the discovery of quantum spin liquid state associated with this model. Consequently, its classical partners such as the Kitaev-Heisenberg (KH) model and associated phase transitions become concerned. Specifically, an intermediate Kosterlitz-Thouless (KT) phase engaged in the transition from the high-temperature (T) disordered state to the low-T sixfold degenerate state is predicted in the isotropic KH model [Phys. Rev. Lett. 109, 187201 (2012)10.1103/PhysRevLett.109.187201], but so far no sufficient experimental proof has been reported. In this work, we consider an essential extension of this KH model on the honeycomb lattice by including the Kitaev exchange anisotropy that is non-negligible in realistic materials. The associated phase transitions are thus investigated using the Monte Carlo simulations. It is found that such an anisotropy will result in a degradation of the sixfold degeneracy of the ground state in the isotropic KH model down to the fourfold or twofold degenerate ground state, and the finite-T phase transitions will also be modified remarkably. Interestingly, the intermediate KT phase can be suppressed by this Kitaev exchange anisotropy. This work thus provides a more realistic description of the physics ingredient with the KH model and presents a possible explanation on absence of the intermediate phase in real materials where the Kitaev exchange anisotropy can be more or less available.