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:1410.4790 · Physical Review B

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

Kazuya Shinjo, Shigetoshi Sota, Takami Tohyama

Published Feb 4, 2015• 36 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physrevb.91.054401

Related papers

Density-Matrix Renormalization Group Study of Kitaev–Heisenberg Model on a Triangular Lattice

Kazuya Shinjo, Shigetoshi Sota, Seiji Yunoki +2 more

We study the Kitaev--Heisenberg model on a triangular lattice by using the two-dimensional density-matrix renormalization group method. Calculating the ground-state energy and spin structure factors, we obtain a ground-state phase diagram of the Kitaev--Heisenberg model. As suggested by previous studies, we find a 120$^\circ$ antiferromagnetic (AFM) phase, a $\mathbb{Z}_2$-vortex crystal phase, a nematic phase, a dual $\mathbb{Z}_2$-vortex crystal phase (the dual counterpart of the $\mathbb{Z}_2$-vortex crystal phase), a $\mathbb{Z}_6$ ferromagnetic phase, and a dual ferromagnetic phase (the dual counterpart of the $\mathbb{Z}_6 $ ferromagnetic phase). Spin correlations discontinuously change at phase boundaries because of first-order phase transitions. We also study the relation among the von Neumann entanglement entropy, entanglement spectrum, and phase transitions of the model. We find that the Schmidt gap closes at phase boundaries and thus the entanglement entropy clearly changes as well. This is different from the Kitaev--Heisenberg model on a honeycomb lattice, where the Schmidt gap and entanglement entropy are not necessarily a good measure of phase transitions.

arXiv:1512.02334•Journal of the Physical Society of Japan•Oct 19, 2016•21 citations

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

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 of the J 1 − J 2 Heisenberg model on the kagome lattice

Fabian Kolley, Stefan Depenbrock, Ian P. McCulloch +2 more

We perform an extensive density-matrix renormalization-group study of the ground-state phase diagram of the spin-$1/2\phantom{\rule{0.16em}{0ex}}{J}_{1}\text{\ensuremath{-}}{J}_{2}$ Heisenberg model on the kagome lattice. We focus on the region of the phase diagram around the kagome Heisenberg antiferromagnet, i.e., at ${J}_{2}=0$. We investigate the static spin structure factor, the magnetic correlation lengths, and the spin gaps. Our results are consistent with the absence of magnetic order in a narrow region around ${J}_{2}\ensuremath{\approx}0$, although strong finite-size effects do not allow us to accurately determine the phase boundaries. This result is in agreement with the presence of an extended spin-liquid region, as it has been proposed recently. Outside the disordered region, we find that for ferromagnetic and antiferromagnetic ${J}_{2}$, the ground state displays signatures of the magnetic order of the $\sqrt{3}\ifmmode\times\else\texttimes\fi{}\sqrt{3}$ and the $q=0$ type, respectively. Finally, we focus on the structure of the entanglement spectrum (ES) in the $q=0$ ordered phase. We discuss the importance of the choice of the bipartition on the finite-size structure of the ES.

arXiv:1410.7911•Physical Review B•Mar 19, 2015•79 citations

Quantum phase diagram of the bilayer Kitaev-Heisenberg model

Elahe Samimi, Antonia Duft, Patrick Adelhardt +2 more

We study the ground-state phase diagram of the spin-$1/2$ Kitaev-Heisenberg model on the bilayer honeycomb lattice with large-scale tensor network calculations based on the infinite projected entangled pair state technique as well as high-order series expansions. We find that beyond various magnetically ordered phases, including ferromagnetic, zigzag, antiferromagnetic (AFM) and stripy states, two extended quantum spin liquid phases arise in the proximity of the Kitaev limit. While these ordered phases also appear in the monolayer Kitaev-Heisenberg model, our results further show that a valence bond solid state emerges in a relatively narrow range of parameter space between the AFM and stripy phases, which can be adiabatically connected to isolated Heisenberg dimers. Our results highlight the importance of considering interlayer interactions on the emergence of novel quantum phases in the bilayer Kitaev materials.

arXiv:2412.17495•Physical review. B./Physical review. B•Apr 16, 2026•0 citations

Ground-state properties of antiferromagnetic anisotropic S=1 Heisenberg spin chains

D. Peters, Ian P. McCulloch, Walter Selke

Using (infinite) density-matrix renormalization-group techniques, ground-state properties of antiferromagnetic $S=1$ Heisenberg spin chains with exchange and single-site anisotropies in an external field are studied. The phase diagram is known to display a plenitude of interesting phases. We elucidate quantum phase transitions between the supersolid and spin-liquid phases as well as the spin-liquid and ferromagnetic phases. Analyzing spin-correlation functions in the spin-liquid phase, commensurate and (two distinct) incommensurate regions are identified.

arXiv:1111.5547•Physical Review B•Feb 22, 2012•12 citations
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∘{120}^{\ensuremath{\circ}}120\ensuremath∘ 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.
We study the Kitaev--Heisenberg model on a triangular lattice by using the two-dimensional density-matrix renormalization group method. Calculating the ground-state energy and spin structure factors, we obtain a ground-state phase diagram of the Kitaev--Heisenberg model. As suggested by previous studies, we find a 120∘^\circ∘ antiferromagnetic (AFM) phase, a Z2\mathbb{Z}_2Z2​-vortex crystal phase, a nematic phase, a dual Z2\mathbb{Z}_2Z2​-vortex crystal phase (the dual counterpart of the Z2\mathbb{Z}_2Z2​-vortex crystal phase), a Z6\mathbb{Z}_6Z6​ ferromagnetic phase, and a dual ferromagnetic phase (the dual counterpart of the $\mathbb{Z}_6 $ ferromagnetic phase). Spin correlations discontinuously change at phase boundaries because of first-order phase transitions. We also study the relation among the von Neumann entanglement entropy, entanglement spectrum, and phase transitions of the model. We find that the Schmidt gap closes at phase boundaries and thus the entanglement entropy clearly changes as well. This is different from the Kitaev--Heisenberg model on a honeycomb lattice, where the Schmidt gap and entanglement entropy are not necessarily a good measure of phase transitions.
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.
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 perform an extensive density-matrix renormalization-group study of the ground-state phase diagram of the spin-$1/2\phantom{\rule{0.16em}{0ex}}{J}_{1}\text{\ensuremath{-}}{J}_{2}$ Heisenberg model on the kagome lattice. We focus on the region of the phase diagram around the kagome Heisenberg antiferromagnet, i.e., at J2=0{J}_{2}=0J2​=0. We investigate the static spin structure factor, the magnetic correlation lengths, and the spin gaps. Our results are consistent with the absence of magnetic order in a narrow region around ${J}_{2}\ensuremath{\approx}0$, although strong finite-size effects do not allow us to accurately determine the phase boundaries. This result is in agreement with the presence of an extended spin-liquid region, as it has been proposed recently. Outside the disordered region, we find that for ferromagnetic and antiferromagnetic J2{J}_{2}J2​, the ground state displays signatures of the magnetic order of the $\sqrt{3}\ifmmode\times\else\texttimes\fi{}\sqrt{3}$ and the q=0q=0q=0 type, respectively. Finally, we focus on the structure of the entanglement spectrum (ES) in the q=0q=0q=0 ordered phase. We discuss the importance of the choice of the bipartition on the finite-size structure of the ES.
We study the ground-state phase diagram of the spin-1/21/21/2 Kitaev-Heisenberg model on the bilayer honeycomb lattice with large-scale tensor network calculations based on the infinite projected entangled pair state technique as well as high-order series expansions. We find that beyond various magnetically ordered phases, including ferromagnetic, zigzag, antiferromagnetic (AFM) and stripy states, two extended quantum spin liquid phases arise in the proximity of the Kitaev limit. While these ordered phases also appear in the monolayer Kitaev-Heisenberg model, our results further show that a valence bond solid state emerges in a relatively narrow range of parameter space between the AFM and stripy phases, which can be adiabatically connected to isolated Heisenberg dimers. Our results highlight the importance of considering interlayer interactions on the emergence of novel quantum phases in the bilayer Kitaev materials.
Using (infinite) density-matrix renormalization-group techniques, ground-state properties of antiferromagnetic S=1S=1S=1 Heisenberg spin chains with exchange and single-site anisotropies in an external field are studied. The phase diagram is known to display a plenitude of interesting phases. We elucidate quantum phase transitions between the supersolid and spin-liquid phases as well as the spin-liquid and ferromagnetic phases. Analyzing spin-correlation functions in the spin-liquid phase, commensurate and (two distinct) incommensurate regions are identified.