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Physical review. B./Physical review. B

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

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

Published Jan 21, 2026• 1 citation
Publisher

Abstract

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.

DOI
10.1103/cglm-2ctt

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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 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.
The higher-spin Kitaev magnets, in which the Kitaev interaction and off-diagonal exchange couplings are overwhelmingly large, have emerged as a fertile avenue to explore exotic phases and unusual excitations. In this paper, we study the quantum phase diagram of the spin-1 Kitaev-$\mathrm{\ensuremath{\Gamma}}$ model on the honeycomb lattice using density-matrix renormalization group. It harbors six distinct phases and the intriguing findings are three magnetically ordered phases in which both time-reversal symmetry and lattice symmetry, albeit of different sorts, are broken spontaneously. The chiral spin state originates from the order-by-disorder effect and exhibits an almost saturated scalar spin chirality at the quantum level. Depending on the relative strength of the two interactions, it also features a columnarlike or plaquettelike dimer pattern as a consequence of the translational symmetry breaking. In parallel, the nematic ferromagnets are situated at the ferromagnetic Kitaev side and possess small but finite ferromagnetic ordering. The lattice-rotational symmetry breaking enforces nonequivalent bond energy along one of the three bonds. Although the intrinsic difference between the two nematic ferromagnets remains elusive, the discontinuities in the von Neumann entropy, hexagonal plaquette operator, and Wilson loop operator convincingly suggest that they are separated via a first-order phase transition.
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.
Kitaev materials are promising materials for hosting quantum spin liquids and investigating the interplay of topological and symmetry-breaking phases.We use an unsupervised and interpretable machine-learning method, the tensorial-kernel support vector machine, to study the honeycomb Kitaev-model in a magnetic field.Our machine learns the global classical phase diagram and the associated analytical order parameters, including several distinct spin liquids, two exotic S 3 magnets, and two modulated S 3 × Z 3 magnets.We find that the extension of Kitaev spin liquids and a field-induced suppression of magnetic order already occur in the large-S limit, implying that critical parts of the physics of Kitaev materials can be understood at the classical level.Moreover, the two S 3 × Z 3 orders are induced by competition between Kitaev and spin liquids and feature a different type of spin-lattice entangled modulation, which requires a matrix description instead of scalar phase factors.Our work provides a direct instance of a machine detecting new phases and paves the way towards the development of automated tools to explore unsolved problems in many-body physics.
Abstract The Kitaev spin liquid, a ground state of the bond-dependent Kitaev model in a honeycomb lattice has been a center of attraction, since a microscopic theory to realize such an interaction in solid-state materials was discovered. A challenge in real materials though is the presence of the Heisenberg and another bond-dependent Gamma interactions detrimental to the Kitaev spin liquid, and there have been many debates on their relative strengths. Here we offer a strategy to extract the Kitaev interaction out of a full microscopic model by utilizing the symmetries of the Hamiltonian. Two tilted magnetic field directions related by a two-fold rotational symmetry generate distinct spin excitations originated from a specific combination of the Kitaev and Gamma interactions. Together with the in- and out-of-plane magnetic anisotropy, one can determine the Kitaev and Gamma interactions separately. Dynamic spin structure factors are presented to motivate future experiments. The proposed setups will advance the search for Kitaev materials.
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.