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:2107.02971 · Physical review. B./Physical review. B

Strain-induced phase diagram of the S=32 Kitaev material CrSiTe3

Zongsheng Zhou, Ken Chen, Qiang Luo, Hong‐Gang Luo, Jize Zhao

Published Dec 20, 2021• 7 citations
arXivHTMLPDF

Abstract

The interplay among anisotropic magnetic terms, such as the bond-dependent Kitaev interactions and single-ion anisotropy, plays a key role in stabilizing the finite-temperature ferromagnetism in the two-dimensional compound ${\mathrm{CrSiTe}}_{3}$. While the Heisenberg interaction is predominant in this material, a recent work shows that it is rather sensitive to the compressive strain, leading to a variety of phases, possibly including a sought-after Kitaev quantum spin liquid [C. Xu et al., Phys. Rev. Lett. 124, 087205 (2020)]. To further understand these states, we establish the quantum phase diagram of a related bond-directional spin-$3/2$ model by the density-matrix renormalization group method. As the Heisenberg coupling varies from ferromagnetic to antiferromagnetic, three magnetically ordered phases, i.e., a ferromagnetic phase, a ${120}^{\ensuremath{\circ}}$ phase, and an antiferromagnetic phase, appear consecutively. All the phases are separated by first-order phase transitions, as revealed by the kinks in the ground-state energy and the jumps in the magnetic order parameters. However, no positive evidence of the quantum spin liquid state is found and possible reasons are discussed briefly.

DOI
10.1103/physrevb.104.214425

Related papers

Quantum phase diagram of the extended spin-3/2 Kitaev-Heisenberg model: A DMRG study

Gui-Xin Liu, Ting-Long Wang, Yi‐Fan Jiang

Recently there has been considerable excitement surrounding the promising realization of high-spin Kitaev material, such as the quasi-2D compound CrI$_3$ and CrGeTe$_3$. However, the stability of quantum spin liquids (QSL) against single ion anisotropy (SIA) in these materials and the global quantum phase diagram of the extended spin-3/2 Kitaev model with finite SIA remain unclear. In this study, we perform large-scale density matrix renormalization group (DMRG) to explore the quantum phase diagram of the generalized spin-3/2 Kitaev-Heisenberg (K-H) model accompanied with SIA $A_c$. In the $A_c=0$ limit, the spin-3/2 K-H model exhibits a quantum phase diagram similar to that of a spin-1/2 system, including two QSLs around antiferromagnetic and ferromagnetic Kitaev models. For models with finite $A_c$, we map out the quantum phase diagram around two Kitaev points and observe distinct types of in-plane vortex orders developed from these two QSL phases. Interestingly, series of nearly degenerate vortex configurations are discovered in each vortex phases. Using linear spin-wave theory, we demonstrate that these vortex configurations can be understood as a consequence of the quantum correction on a continuous family of degenerate classical states.

arXiv:2503.24246•Mar 31, 2025•0 citations

Competing magnetic and topological orders in the spin-1 Kitaev-Heisenberg chain with single-ion anisotropy

Sahinur Reja, Satoshi Nishimoto

We investigate the ground-state phase diagram of the spin-1 Kitaev–Heisenberg (KH) chain in the presence of uniaxial single-ion anisotropy D z using the density-matrix renormalization-group method. The relative strength of the Heisenberg and Kitaev interactions is parametrized by a coupling angle ϕ , defined by J = cos ϕ and K = sin ϕ . By combining energy-based diagnostics with finite-size extrapolations of order parameters and correlation functions, we obtain a comprehensive phase diagram as a function of ϕ and D z . The phase diagram contains ferromagnetic and Néel ordered phases, collinear states with four-site spin modulation, magnetically disordered or critical regimes, two Kitaev-dominated spin-liquid-like regions, and a topological Haldane phase near the Heisenberg limit. We find that the Kitaev-dominated disordered regions acquire finite parameter widths in the spin-1 model, whereas the Haldane phase is fragile against Kitaev-type anisotropy, especially for D z < 0 . Positive D z generally suppresses magnetic order and expands nonmagnetic regimes, while negative D z enhances Ising-like magnetic order. At D z = 0 , we also identify an exactly solvable point at tan ϕ = − 2 ( ϕ / π ≃ 1.6476 ) , which gives rise to a first-order transition between the Néel- z state and a four-site collinear state. We further contrast these findings with the spin- 1 / 2 KH chain and with the spin-1 honeycomb KH model, highlighting the distinct roles of single-ion anisotropy and dimensionality in Kitaev-type magnets.

arXiv:2512.20912•Physical review. B./Physical review. B•Jul 20, 2026•0 citations

Ground-state phase diagram of spin- S Kitaev-Heisenberg models

Kiyu Fukui, Yasuyuki Kato, Joji Nasu +1 more

The Kitaev model, whose ground state is a quantum spin liquid (QSL), was originally conceived for spin $S=1/2$ moments on a honeycomb lattice. In recent years, the model has been extended to higher $S$ from both theoretical and experimental interests, but the stability of the QSL ground state has not been systematically clarified for general $S$, especially in the presence of other additional interactions, which inevitably exist in candidate materials. Here we study the spin-$S$ Kitaev-Heisenberg models by using an extension of the pseudofermion functional renormalization group method to general $S$. We show that, similar to the $S=1/2$ case, the phase diagram for higher $S$ contains the QSL phases in the vicinities of the pristine ferromagnetic and antiferromagnetic Kitaev models, in addition to four magnetically ordered phases. We find, however, that the QSL phases shrink rapidly with increasing $S$, becoming vanishingly narrow for $S\ensuremath{\ge}2$, whereas the phase boundaries between the ordered phases remain almost intact. Our results provide a reference for the search for higher-$S$ Kitaev materials.

arXiv:2207.03786•Physical review. B./Physical review. B•Nov 16, 2022•31 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

Ground-State Phase Diagram of the Kitaev–Heisenberg Model on a Three-dimensional Hyperhoneycomb Lattice

Kiyu Fukui, Yasuyuki Kato, Yukitoshi Motome

The Kitaev model, which hosts a quantum spin liquid (QSL) in the ground state, was originally defined on a two-dimensional honeycomb lattice, but can be straightforwardly extended to any tricoordinate lattices in any spatial dimensions. In particular, the three-dimensional (3D) extensions are of interest as a realization of 3D QSLs, and some materials like $β$-Li$_{2}$IrO$_{3}$, $γ$-Li$_2$IrO$_3$, and $β$-ZnIrO$_{3}$ were proposed for the candidates. However, the phase diagrams of the models for those candidates have not been fully elucidated, mainly due to the limitation of numerical methods for 3D frustrated quantum spin systems. Here we study the Kitaev-Heisenberg model defined on a 3D hyperhoneycomb lattice, by using the pseudofermion functional renormalization group method. We show that the ground-state phase diagram contains the QSL phases in the vicinities of the pristine ferromagnetic and antiferromagnetic Kitaev models, in addition to four magnetically ordered phases, similar to the two-dimensional honeycomb case. Our results respect the four-sublattice symmetry inherent in the model, which was violated in the previous study. Moreover, we also show how the phase diagram changes with the anisotropy in the interactions. The results provide a reference for the search of the hyperhoneycomb Kitaev materials.

arXiv:2303.09156•Journal of the Physical Society of Japan•May 26, 2023•8 citations

Density-matrix renormalization group study of the extended Kitaev-Heisenberg model

Kazuya Shinjo, Shigetoshi Sota, Takami Tohyama

We study an extended Kitaev-Heisenberg model including additional anisotropic couplings by using the two-dimensional density-matrix renormalization group method. Calculating the ground-state energy, entanglement entropy, and spin-spin correlation functions, we make a phase diagram of the extended Kitaev-Heisenberg model around the spin-liquid phase. We find a zigzag antiferromagnetic phase, a ferromagnetic phase, a ${120}^{\ensuremath{\circ}}$ antiferromagnetic phase, and two kinds of incommensurate phases around the Kitaev spin-liquid phase. Furthermore, we study the entanglement spectrum of the model, and we find that entanglement levels in the Kitaev spin-liquid phase are degenerate forming pairs, but those in the magnetically ordered phases are nondegenerate. The Schmidt gap defined as the energy difference between the lowest two levels changes at the phase boundary adjacent to the Kitaev spin-liquid phase. However, we find that phase boundaries between magnetically ordered phases do not necessarily agree with the change of the Schmidt gap.

arXiv:1410.4790•Physical Review B•Feb 4, 2015•36 citations
The interplay among anisotropic magnetic terms, such as the bond-dependent Kitaev interactions and single-ion anisotropy, plays a key role in stabilizing the finite-temperature ferromagnetism in the two-dimensional compound CrSiTe3{\mathrm{CrSiTe}}_{3}CrSiTe3​. While the Heisenberg interaction is predominant in this material, a recent work shows that it is rather sensitive to the compressive strain, leading to a variety of phases, possibly including a sought-after Kitaev quantum spin liquid [C. Xu et al., Phys. Rev. Lett. 124, 087205 (2020)]. To further understand these states, we establish the quantum phase diagram of a related bond-directional spin-3/23/23/2 model by the density-matrix renormalization group method. As the Heisenberg coupling varies from ferromagnetic to antiferromagnetic, three magnetically ordered phases, i.e., a ferromagnetic phase, a 120\ensuremath∘{120}^{\ensuremath{\circ}}120\ensuremath∘ phase, and an antiferromagnetic phase, appear consecutively. All the phases are separated by first-order phase transitions, as revealed by the kinks in the ground-state energy and the jumps in the magnetic order parameters. However, no positive evidence of the quantum spin liquid state is found and possible reasons are discussed briefly.
Recently there has been considerable excitement surrounding the promising realization of high-spin Kitaev material, such as the quasi-2D compound CrI3_33​ and CrGeTe3_33​. However, the stability of quantum spin liquids (QSL) against single ion anisotropy (SIA) in these materials and the global quantum phase diagram of the extended spin-3/2 Kitaev model with finite SIA remain unclear. In this study, we perform large-scale density matrix renormalization group (DMRG) to explore the quantum phase diagram of the generalized spin-3/2 Kitaev-Heisenberg (K-H) model accompanied with SIA AcA_cAc​. In the Ac=0A_c=0Ac​=0 limit, the spin-3/2 K-H model exhibits a quantum phase diagram similar to that of a spin-1/2 system, including two QSLs around antiferromagnetic and ferromagnetic Kitaev models. For models with finite AcA_cAc​, we map out the quantum phase diagram around two Kitaev points and observe distinct types of in-plane vortex orders developed from these two QSL phases. Interestingly, series of nearly degenerate vortex configurations are discovered in each vortex phases. Using linear spin-wave theory, we demonstrate that these vortex configurations can be understood as a consequence of the quantum correction on a continuous family of degenerate classical states.
We investigate the ground-state phase diagram of the spin-1 Kitaev–Heisenberg (KH) chain in the presence of uniaxial single-ion anisotropy D z using the density-matrix renormalization-group method. The relative strength of the Heisenberg and Kitaev interactions is parametrized by a coupling angle ϕ , defined by J = cos ϕ and K = sin ϕ . By combining energy-based diagnostics with finite-size extrapolations of order parameters and correlation functions, we obtain a comprehensive phase diagram as a function of ϕ and D z . The phase diagram contains ferromagnetic and Néel ordered phases, collinear states with four-site spin modulation, magnetically disordered or critical regimes, two Kitaev-dominated spin-liquid-like regions, and a topological Haldane phase near the Heisenberg limit. We find that the Kitaev-dominated disordered regions acquire finite parameter widths in the spin-1 model, whereas the Haldane phase is fragile against Kitaev-type anisotropy, especially for D z < 0 . Positive D z generally suppresses magnetic order and expands nonmagnetic regimes, while negative D z enhances Ising-like magnetic order. At D z = 0 , we also identify an exactly solvable point at tan ϕ = − 2 ( ϕ / π ≃ 1.6476 ) , which gives rise to a first-order transition between the Néel- z state and a four-site collinear state. We further contrast these findings with the spin- 1 / 2 KH chain and with the spin-1 honeycomb KH model, highlighting the distinct roles of single-ion anisotropy and dimensionality in Kitaev-type magnets.
The Kitaev model, whose ground state is a quantum spin liquid (QSL), was originally conceived for spin S=1/2S=1/2S=1/2 moments on a honeycomb lattice. In recent years, the model has been extended to higher SSS from both theoretical and experimental interests, but the stability of the QSL ground state has not been systematically clarified for general SSS, especially in the presence of other additional interactions, which inevitably exist in candidate materials. Here we study the spin-SSS Kitaev-Heisenberg models by using an extension of the pseudofermion functional renormalization group method to general SSS. We show that, similar to the S=1/2S=1/2S=1/2 case, the phase diagram for higher SSS contains the QSL phases in the vicinities of the pristine ferromagnetic and antiferromagnetic Kitaev models, in addition to four magnetically ordered phases. We find, however, that the QSL phases shrink rapidly with increasing SSS, becoming vanishingly narrow for $S\ensuremath{\ge}2$, whereas the phase boundaries between the ordered phases remain almost intact. Our results provide a reference for the search for higher-SSS Kitaev materials.
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.
The Kitaev model, which hosts a quantum spin liquid (QSL) in the ground state, was originally defined on a two-dimensional honeycomb lattice, but can be straightforwardly extended to any tricoordinate lattices in any spatial dimensions. In particular, the three-dimensional (3D) extensions are of interest as a realization of 3D QSLs, and some materials like βββ-Li2_{2}2​IrO3_{3}3​, γγγ-Li2_22​IrO3_33​, and βββ-ZnIrO3_{3}3​ were proposed for the candidates. However, the phase diagrams of the models for those candidates have not been fully elucidated, mainly due to the limitation of numerical methods for 3D frustrated quantum spin systems. Here we study the Kitaev-Heisenberg model defined on a 3D hyperhoneycomb lattice, by using the pseudofermion functional renormalization group method. We show that the ground-state phase diagram contains the QSL phases in the vicinities of the pristine ferromagnetic and antiferromagnetic Kitaev models, in addition to four magnetically ordered phases, similar to the two-dimensional honeycomb case. Our results respect the four-sublattice symmetry inherent in the model, which was violated in the previous study. Moreover, we also show how the phase diagram changes with the anisotropy in the interactions. The results provide a reference for the search of the hyperhoneycomb Kitaev materials.
We study an extended Kitaev-Heisenberg model including additional anisotropic couplings by using the two-dimensional density-matrix renormalization group method. Calculating the ground-state energy, entanglement entropy, and spin-spin correlation functions, we make a phase diagram of the extended Kitaev-Heisenberg model around the spin-liquid phase. We find a zigzag antiferromagnetic phase, a ferromagnetic phase, a ${120}^{\ensuremath{\circ}}$ antiferromagnetic phase, and two kinds of incommensurate phases around the Kitaev spin-liquid phase. Furthermore, we study the entanglement spectrum of the model, and we find that entanglement levels in the Kitaev spin-liquid phase are degenerate forming pairs, but those in the magnetically ordered phases are nondegenerate. The Schmidt gap defined as the energy difference between the lowest two levels changes at the phase boundary adjacent to the Kitaev spin-liquid phase. However, we find that phase boundaries between magnetically ordered phases do not necessarily agree with the change of the Schmidt gap.