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:2304.09891 · Physical review. B./Physical review. B

Vison crystals, chiral, and crystalline phases in the Yao-Lee model

Muhammad Akram, Emilian M. Nica, Yuan-Ming Lu, Onur Erten

Published Dec 20, 2023• 15 citations
arXivHTMLPDF

Abstract

We study the phase diagram of the Yao-Lee model with Kitaev-type spin-orbital interactions in the presence of Dzyaloshinskii-Moriya interactions and external magnetic fields. Unlike the Kitaev model, the Yao-Lee model can still be solved exactly under these perturbations due to the enlarged local Hilbert space. Through a variational analysis, we obtain a rich ground-state phase diagram that consists of a variety of vison crystals with periodic arrangements of background ${\mathbb{Z}}_{2}$ flux (i.e., visons). With an out-of-plane magnetic field, these phases have gapped bulk and chiral edge states, characterized by a Chern number $\ensuremath{\nu}$ and an associated chiral central charge ${c}_{\ensuremath{-}}=\ensuremath{\nu}/2$ of edge states. We also find helical Majorana edge states that are protected by magnetic mirror symmetry. For the bilayer systems, we find that interlayer coupling can also stabilize new topological phases. Our results spotlight the tunability and the accompanying rich physics in exactly solvable spin-orbital generalizations of the Kitaev model.

DOI
10.1103/physrevb.108.224427

Related papers

Thermodynamics of vison crystals in an anisotropic quantum spin liquid

Ritwika Majumder, Onur Erten, Anamitra Mukherjee

Using unbiased Monte Carlo simulations and variational analysis, we present the ground state and finite-temperature phase diagrams of an exactly solvable spin-orbital model with Kitaev-type interactions on a square lattice. We show that an array of gapped and gapless vison crystals, characterized by the periodic arrangement of ${\mathbb{Z}}_{2}$ flux excitations, can be stabilized as a function of external magnetic field and exchange anisotropy. In particular, we discover a variety of ``quarter phases'' wherein different 16-site periodic patterns emerge, with only a quarter of the fluxes adopting zero-flux configurations. In contrast, the rest remain in $\ensuremath{\pi}$-flux configurations. Vison crystals break translational symmetry and undergo finite-temperature phase transitions. We investigate the finite-temperature properties of these phases and report the corresponding critical and crossover temperatures. Our results reveal an array of novel phases in exactly solvable extensions of the Kitaev model, wherein local and topological orders can coexist.

arXiv:2401.14525•Physical review. B./Physical review. B•Sep 30, 2024•5 citations

Topological transitions in the Yao-Lee spin-orbital model and effects of site disorder

Vladislav Poliakov, Wen-Han Kao, Natalia Borisovna Perkins

The Yao-Lee model is an example of exactly solvable spin-orbital models that are generalizations of the original Kitaev honeycomb model with extra local orbital degrees of freedom. Similarly to the Kitaev model, both spin and orbital degrees of freedom are effectively represented using sets of three-flavored Majorana fermions. The Yao-Lee model exhibits a quantum spin liquid ground state with gapped and immobile ${Z}_{2}$ fluxes and threefold degenerate itinerant Majorana fermions. Our work demonstrated that by introducing different time-reversal-symmetry- (TRS) breaking fields one can split the degeneracy of Majorana fermions and close the gap for some of the bands, thus changing its topology. We calculated a comprehensive topological phase diagram for the Yao-Lee model by considering various combinations of TRS-breaking fields. This investigation revealed the emergence of distinct topological regions, each separated by nodal lines, signifying an evolution in the model's topological properties. We also investigated the impact of vacancies in the system. Our findings revealed that while vacancies modify the low-energy spectrum of the model, their presence has a limited impact on the topological properties of the model, at least for small-enough concentrations.

arXiv:2312.17359•Physical review. B./Physical review. B•Aug 8, 2024•11 citations

Magnetically ordered yet topologically robust phases emerging in concurrent Kitaev spin liquids

Muhammad Akram, Aayush Vijayvargia, Hae‐Young Kee +1 more

Spin-orbital generalizations of Kitaev model, such as Yao-Lee model, have attracted recent attention due to their enhanced stability of spin liquid phases against perturbations. Motivated by microscopic calculations for the realization of Yao-Lee model showing additional interactions, we study the phase diagram of the Yao-Lee model with added Kitaev and Heisenberg terms. While the plaquette operator is conserved even in the presence of added perturbations, the model becomes no longer exactly solvable. Using perturbation and Majorana mean-field theory, we find magnetic order can arise in the spin sector while the orbital sector remains a liquid for dominant Kitaev interactions, whereas both sectors form liquid phases when Yao-Lee interactions dominate. Additional Heisenberg exchange can enhance or suppress the magnetic order, revealing a rich coexistence of magnetic and topological phases.

arXiv:2507.21226•npj Quantum Materials•Jun 25, 2026•2 citations

Exactly solvable spin liquids in Kitaev bilayers and moiré superlattices

Ivan Dutta, Anamitra Mukherjee, Onur Erten +1 more

Building on the recent advancements on moir\'e superlattices, we propose an exactly solvable model with Kitaev-type interactions on a bilayer honeycomb lattice for both AA stacking and moir\'e superlattices. Using Monte Carlo simulations and variational analysis, we uncover a rich variety of phases where the intra and interlayer ${\mathbb{Z}}_{2}$ fluxes (visons) are arranged in a periodic fashion in the ground state, tuned by interlayer coupling and out-of-plane external magnetic field. We further extend our model to moir\'e superlattices at various commensurate twist angles around two distinct twist centers represented by ${C}_{3z}$ and ${C}_{6z}$ of the honeycomb lattice. Our simulations reveal generalized arrangements of plaquette values that correlate with the AA or AB stacking regions across the moir\'e unit cell. Moreover, we find that, depending on the twist angle, twist center and interlayer coupling, moir\'e superlattices exhibit to a variety of gapped and gapless spin liquid phases and can also host corner and edge modes. Our results highlight the rich physics in bilayer and twisted bilayer models of exactly solvable quantum spin liquids.

arXiv:2506.04181•Physical review. B./Physical review. B•Nov 19, 2025•0 citations

Generation of chirality and orbital magnetization by Stone-Wales-type lattice defects in the Kitaev spin liquid

Arnab Seth, Fay Borhani, Itamar Kimchi

In this work we extend our study of the effect of certain crystallographic defects on the spin-1/2 Kitaev honeycomb spin liquid (arXiv:2511.19409), focusing on its gapless phase and contrasting with the gapped phase. We identify a Stone-Wales (SW) local defect consisting of a 90$^\circ$ bond rotation that preserves Kitaev bond labels for edge-sharing octahedra and thereby enables exact solvability. These SW-type defects involve odd-sided plaquettes with $\pm π/2$ fluxes, but can be created locally. An isolated defect hosts a time-reversal pair of ground-state flux configurations with large net chirality. Certain excitations are also chiral. The chirality manifests in Majorana local Chern marker and in scalar spin chirality, producing electronic orbital magnetization. T-matrix analysis and numerics at finite defect density $n_d$ show that defect chiralities generate a topological gap of $11 n_d$ protecting a Chern number $C=\pm 1$. Emergent ferromagnetic long range Ising interactions $r^{-γ}$ with $2<γ< 3$ between defect chiralities lead to a finite temperature $T_c$ phase transition into the chiral spin liquid. The $T_c$ is proportional to $n_d$ and diverges when $γ\rightarrow 2$. We also consider additional solvable impurity potentials and find that $γ$ can be reduced to below $2.3$ and correspondingly enhance $T_c$. Our results offer applications to 2D Dirac cone systems with a finite density of fluctuating Ising magnetic impurities and to identifying spin liquids with lattice defects.

arXiv:2512.13490•Physical review. B./Physical review. B•Apr 20, 2026•0 citations

Frustrated magnetic order in hybrid Kitaev spin-orbital models

Ivan Dutta, Aayush Vijayvargia, Anamitra Mukherjee +2 more

Spin-orbital generalization of Kitaev model provides a robust extension to the original Kitaev model. However, real materials often exhibit competing interactions that break exact solvability which can give rise to new phases. Motivated by recent microscopic proposals of coexisting Yao-Lee and Kitaev couplings, we investigate the fate of the ground state when two independent exactly solvable spin liquid Hamiltonians each originally formulated on different lattice geometries are combined on a common lattice environment. We first focus on the hybrid Kitaev's honeycomb and square-lattice model. Using self-consistent mean-field analysis and perturbative calculation, we show that the strong-Kitaev regime yields magnetic order in the spin sector, while the orbital sector retains its topological order. We further analyze the hybridization of the Yao-Lee and square-lattice models and find that the model exhibits a rich evolution of Majorana Dirac bands and Lifshitz transitions. Remarkably, when the Yao-Lee and square-lattice couplings are equal and opposite, the model restores its exact solvability with a single itinerant Majorana flavor. These results demonstrate that hybrid spin liquid platforms may host various emergent phases beyond conventional exactly solvable limits.

arXiv:2605.05196•May 6, 2026•0 citations
We study the phase diagram of the Yao-Lee model with Kitaev-type spin-orbital interactions in the presence of Dzyaloshinskii-Moriya interactions and external magnetic fields. Unlike the Kitaev model, the Yao-Lee model can still be solved exactly under these perturbations due to the enlarged local Hilbert space. Through a variational analysis, we obtain a rich ground-state phase diagram that consists of a variety of vison crystals with periodic arrangements of background Z2{\mathbb{Z}}_{2}Z2​ flux (i.e., visons). With an out-of-plane magnetic field, these phases have gapped bulk and chiral edge states, characterized by a Chern number \ensuremathν\ensuremath{\nu}\ensuremathν and an associated chiral central charge c\ensuremath−=\ensuremathν/2{c}_{\ensuremath{-}}=\ensuremath{\nu}/2c\ensuremath−​=\ensuremathν/2 of edge states. We also find helical Majorana edge states that are protected by magnetic mirror symmetry. For the bilayer systems, we find that interlayer coupling can also stabilize new topological phases. Our results spotlight the tunability and the accompanying rich physics in exactly solvable spin-orbital generalizations of the Kitaev model.
Using unbiased Monte Carlo simulations and variational analysis, we present the ground state and finite-temperature phase diagrams of an exactly solvable spin-orbital model with Kitaev-type interactions on a square lattice. We show that an array of gapped and gapless vison crystals, characterized by the periodic arrangement of Z2{\mathbb{Z}}_{2}Z2​ flux excitations, can be stabilized as a function of external magnetic field and exchange anisotropy. In particular, we discover a variety of ``quarter phases'' wherein different 16-site periodic patterns emerge, with only a quarter of the fluxes adopting zero-flux configurations. In contrast, the rest remain in $\ensuremath{\pi}$-flux configurations. Vison crystals break translational symmetry and undergo finite-temperature phase transitions. We investigate the finite-temperature properties of these phases and report the corresponding critical and crossover temperatures. Our results reveal an array of novel phases in exactly solvable extensions of the Kitaev model, wherein local and topological orders can coexist.
The Yao-Lee model is an example of exactly solvable spin-orbital models that are generalizations of the original Kitaev honeycomb model with extra local orbital degrees of freedom. Similarly to the Kitaev model, both spin and orbital degrees of freedom are effectively represented using sets of three-flavored Majorana fermions. The Yao-Lee model exhibits a quantum spin liquid ground state with gapped and immobile Z2{Z}_{2}Z2​ fluxes and threefold degenerate itinerant Majorana fermions. Our work demonstrated that by introducing different time-reversal-symmetry- (TRS) breaking fields one can split the degeneracy of Majorana fermions and close the gap for some of the bands, thus changing its topology. We calculated a comprehensive topological phase diagram for the Yao-Lee model by considering various combinations of TRS-breaking fields. This investigation revealed the emergence of distinct topological regions, each separated by nodal lines, signifying an evolution in the model's topological properties. We also investigated the impact of vacancies in the system. Our findings revealed that while vacancies modify the low-energy spectrum of the model, their presence has a limited impact on the topological properties of the model, at least for small-enough concentrations.
Spin-orbital generalizations of Kitaev model, such as Yao-Lee model, have attracted recent attention due to their enhanced stability of spin liquid phases against perturbations. Motivated by microscopic calculations for the realization of Yao-Lee model showing additional interactions, we study the phase diagram of the Yao-Lee model with added Kitaev and Heisenberg terms. While the plaquette operator is conserved even in the presence of added perturbations, the model becomes no longer exactly solvable. Using perturbation and Majorana mean-field theory, we find magnetic order can arise in the spin sector while the orbital sector remains a liquid for dominant Kitaev interactions, whereas both sectors form liquid phases when Yao-Lee interactions dominate. Additional Heisenberg exchange can enhance or suppress the magnetic order, revealing a rich coexistence of magnetic and topological phases.
Building on the recent advancements on moir\'e superlattices, we propose an exactly solvable model with Kitaev-type interactions on a bilayer honeycomb lattice for both AA stacking and moir\'e superlattices. Using Monte Carlo simulations and variational analysis, we uncover a rich variety of phases where the intra and interlayer Z2{\mathbb{Z}}_{2}Z2​ fluxes (visons) are arranged in a periodic fashion in the ground state, tuned by interlayer coupling and out-of-plane external magnetic field. We further extend our model to moir\'e superlattices at various commensurate twist angles around two distinct twist centers represented by C3z{C}_{3z}C3z​ and C6z{C}_{6z}C6z​ of the honeycomb lattice. Our simulations reveal generalized arrangements of plaquette values that correlate with the AA or AB stacking regions across the moir\'e unit cell. Moreover, we find that, depending on the twist angle, twist center and interlayer coupling, moir\'e superlattices exhibit to a variety of gapped and gapless spin liquid phases and can also host corner and edge modes. Our results highlight the rich physics in bilayer and twisted bilayer models of exactly solvable quantum spin liquids.
In this work we extend our study of the effect of certain crystallographic defects on the spin-1/2 Kitaev honeycomb spin liquid (arXiv:2511.19409), focusing on its gapless phase and contrasting with the gapped phase. We identify a Stone-Wales (SW) local defect consisting of a 90∘^\circ∘ bond rotation that preserves Kitaev bond labels for edge-sharing octahedra and thereby enables exact solvability. These SW-type defects involve odd-sided plaquettes with ±π/2\pm π/2±π/2 fluxes, but can be created locally. An isolated defect hosts a time-reversal pair of ground-state flux configurations with large net chirality. Certain excitations are also chiral. The chirality manifests in Majorana local Chern marker and in scalar spin chirality, producing electronic orbital magnetization. T-matrix analysis and numerics at finite defect density ndn_dnd​ show that defect chiralities generate a topological gap of 11nd11 n_d11nd​ protecting a Chern number C=±1C=\pm 1C=±1. Emergent ferromagnetic long range Ising interactions r−γr^{-γ}r−γ with 2<γ<32<γ< 32<γ<3 between defect chiralities lead to a finite temperature TcT_cTc​ phase transition into the chiral spin liquid. The TcT_cTc​ is proportional to ndn_dnd​ and diverges when γ→2γ\rightarrow 2γ→2. We also consider additional solvable impurity potentials and find that γγγ can be reduced to below 2.32.32.3 and correspondingly enhance TcT_cTc​. Our results offer applications to 2D Dirac cone systems with a finite density of fluctuating Ising magnetic impurities and to identifying spin liquids with lattice defects.
Spin-orbital generalization of Kitaev model provides a robust extension to the original Kitaev model. However, real materials often exhibit competing interactions that break exact solvability which can give rise to new phases. Motivated by recent microscopic proposals of coexisting Yao-Lee and Kitaev couplings, we investigate the fate of the ground state when two independent exactly solvable spin liquid Hamiltonians each originally formulated on different lattice geometries are combined on a common lattice environment. We first focus on the hybrid Kitaev's honeycomb and square-lattice model. Using self-consistent mean-field analysis and perturbative calculation, we show that the strong-Kitaev regime yields magnetic order in the spin sector, while the orbital sector retains its topological order. We further analyze the hybridization of the Yao-Lee and square-lattice models and find that the model exhibits a rich evolution of Majorana Dirac bands and Lifshitz transitions. Remarkably, when the Yao-Lee and square-lattice couplings are equal and opposite, the model restores its exact solvability with a single itinerant Majorana flavor. These results demonstrate that hybrid spin liquid platforms may host various emergent phases beyond conventional exactly solvable limits.