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:2512.13490 · Physical review. B./Physical review. B

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

Arnab Seth, Fay Borhani, Itamar Kimchi

Published Apr 20, 2026• 0 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/j154-s9qr

Related papers

Chiral Spin Liquid Instability of the Kitaev Honeycomb Model with Crystallographic Defects

Arnab Seth, Fay Borhani, Itamar Kimchi

We study the spin-1/2 Kitaev honeycomb gapless spin liquid in the presence of Stone-Wales-type local lattice defects with odd-sided plaquettes. While the clean Kitaev model has no finite-temperature phase transitions, we find that introducing a finite defect density n_{d}≈10^{-4}-10^{-2} produces a true phase transition with a sizeable T_{c}≈2n_{d} in units of the Kitaev exchange. The resulting non-Abelian chiral quantum spin liquid exhibits scalar spin chirality and electron orbital magnetization which peak near lattice defects. This disorder-driven instability relies on an emergent long range ferromagnetic interaction r^{-γ} (γ≈2.7) between defect chiralities, mediated by the nearly gapless fermions, with implications for topology generation in Dirac cones with fluctuating mass terms.

arXiv:2511.19409•Physical Review Letters•Apr 28, 2026•0 citations

Gapless excitations in Kitaev materials with defects

Lucas R. D. Freitas

A quantum spin liquid is a magnetic phase of matter that is remarkable for its ground state long-range entanglement and fractional excitations. A quantum spin liquid appears in the well-known Kitaev honeycomb spin-half model. In a magnetic field, there is a phase transition to a topological phase with an energy gap in the bulk and chiral Majorana fermions at the edge. However, recent nuclear magnetic resonance experiments suggest excitations without a gap in this phase, signalled by the cubic temperature dependence of the spin-lattice relaxation rate at low temperatures. In this work, I propose a mechanism to account for this experimental result. I use the localization of chiral Majorana modes in defects to explain the presence of gapless modes in the bulk. Treating the weak interaction between the chiral modes in the defects within a mean-field approximation, I find that these modes remain gapless when the interaction is below a critical value that depends on the magnetic field strength. I used the effective low-energy theory to calculate the spin-lattice relaxation rate and found a behavior that agrees with the experimental result.

•Mar 26, 2021•0 citations

Non-Abelian chiral spin liquid on a simple non-Archimedean lattice

Valerio Peri, Seulgi Ok, Stepan S. Tsirkin +5 more

We extend the scope of Kitaev spin liquids to non-Archimedean lattices. For the pentaheptite lattice, which results from the proliferation of Stone-Wales defects on the honeycomb lattice, we find an exactly solvable non-Abelian chiral spin liquid with spontaneous time-reversal symmetry breaking due to lattice loops of odd length. Our findings call for potential extensions of exact results for Kitaev models which are based on reflection positivity, which is not fulfilled by the pentaheptite lattice. We further elaborate on potential realizations of our chiral spin-liquid proposal in strained $\ensuremath{\alpha}\text{\ensuremath{-}}{\mathrm{RuCl}}_{3}$.

arXiv:1908.05280•Physical review. B./Physical review. B•Jan 30, 2020•18 citations

Vacancies in Kitaev quantum spin liquids on the three-dimensional hyperhoneycomb lattice

G. J. Sreejith, Subhro Bhattacharjee, Roderich Moessner

We study the effect of adding disorder to the Kitaev model on the hyperhoneycomb lattice, which hosts both gapped and gapless spin liquid phases with an emergent ${\mathbb{Z}}_{2}$ gauge field. The latter has an unusual gapless spectrum of Majorana fermion excitations, with a co-dimension-two Fermi ring. We thus address the question of the interplay of topological physics and disorder by considering the properties of isolated single and pairs of vacancies. We show that near the vacancies, the local magnetic response to a field ${h}_{z}$ is parametrically enhanced in comparison to the pristine bulk. Unlike the previously studied case of the 2D honeycomb Kitaev model, the vacancies do not bind a flux of the ${\mathbb{Z}}_{2}$ gauge field. In the gapped phase, an isolated vacancy gives rise to effectively free spin-half moments with a nonuniversal coupling to an external field. In the gapless phase, the low-field magnetization is suppressed parametrically to ${(\ensuremath{-}ln{h}_{z})}^{\ensuremath{-}1/2}$ because of interactions with the surrounding spin liquid. We also show that a pair of vacancies is subject to a sublattice-dependent interaction on account of coupling through the bulk spin liquid, which is spatially anisotropic even when all Kitaev couplings have equal strength. This coupling is thus exponentially suppressed with distance in the gapped phase. In the gapless phase, two vacancies on the same (opposite) sublattice exhibit an enhanced (suppressed) low-field response, amounting to an effectively (anti-)ferromagnetic interaction.

arXiv:1512.05266•Physical review. B./Physical review. B•Feb 26, 2016•18 citations

Half-Quantized Thermal Hall Conductance as a Unique Fingerprint of the Non-Abelian Ising Anyon Sector in Kitaev Spin Liquids

Rowan Brad Quni-Gudzinas

In the Kitaev honeycomb model, a weak magnetic field gaps the gapless Majorana cone, driving the system into a gapped non-Abelian phase with Ising topological order. The edge supports a single chiral Majorana mode with chiral central charge $c_- = 1/2$, yielding a half-quantized thermal Hall conductance $\kappa_{xy}/T = \pi^2 k_B^2/6h$. We rigorously investigate whether observing this half-quantized value uniquely identifies the non-Abelian Ising anyon sector, or whether Abelian topological orders or extrinsic mechanisms can produce the same signature. By combining the edge-bulk correspondence with the classification of strictly two-dimensional bosonic topological orders, we show that a chiral central charge $c_-=1/2$ (mod 8) is the unique fingerprint of the Ising non-Abelian anyon theory among minimal bosonic topological orders. Abelian bosonic orders necessarily have integer $c_-$, with the minimal nonzero value being $c_-=1$. Thus, a robustly half-quantized $\kappa_{xy}/T$ uniquely distinguishes the Majorana sector from Abelian alternatives, provided the system is a genuine 2D bosonic spin system free of invertible $E_8$ stacking or phonon contamination. ## 1. Introduction The Kitaev honeycomb model is an exactly solvable model of a quantum spin liquid, characterized by fractionalized excitations known as anyons. In the absence of a magnetic field, the model hosts a gapless Majorana cone. A weak magnetic field in the [111] direction gaps this cone and induces a non-Abelian phase with Ising topological order. This phase supports a single chiral Majorana edge mode, which contributes to a quantized thermal Hall conductance. The central question addressed in this preprint is whether the observation of a half-quantized thermal Hall conductance, corresponding to a chiral central charge $c_- = 1/2$, uniquely identifies the non-Abelian Ising anyon sector, or if Abelian topological orders can mimic this signature. ## 2. Background The thermal Hall conductance $\kappa_{x

•Sep 7, 2026•0 citations

Majorana corner modes in a second-order Kitaev spin liquid

Vatsal Dwivedi, Ciarán Hickey, Tim Eschmann +1 more

Higher-order topological insulators are distinguished by the existence of topologically protected modes with codimension two or higher. Here, we report the manifestation of a second-order topological insulator in a two dimensional frustrated quantum magnet, which exhibits topological corner modes. Our exactly solvable model is a generalization of the Kitaev honeycomb model to the Shastry-Sutherland lattice that, besides a chiral spin liquid phase, exhibits a gapped spin liquid with Majorana corner modes, which are protected by two mirror symmetries. This second-order Kitaev spin liquid remains stable in the presence of thermal fluctuations and undergoes a finite-temperature phase transition evidenced in large-scale quantum Monte Carlo simulations.

arXiv:1803.08922•Physical review. B./Physical review. B•Aug 30, 2018•50 citations
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.
We study the spin-1/2 Kitaev honeycomb gapless spin liquid in the presence of Stone-Wales-type local lattice defects with odd-sided plaquettes. While the clean Kitaev model has no finite-temperature phase transitions, we find that introducing a finite defect density n_{d}≈10^{-4}-10^{-2} produces a true phase transition with a sizeable T_{c}≈2n_{d} in units of the Kitaev exchange. The resulting non-Abelian chiral quantum spin liquid exhibits scalar spin chirality and electron orbital magnetization which peak near lattice defects. This disorder-driven instability relies on an emergent long range ferromagnetic interaction r^{-γ} (γ≈2.7) between defect chiralities, mediated by the nearly gapless fermions, with implications for topology generation in Dirac cones with fluctuating mass terms.
A quantum spin liquid is a magnetic phase of matter that is remarkable for its ground state long-range entanglement and fractional excitations. A quantum spin liquid appears in the well-known Kitaev honeycomb spin-half model. In a magnetic field, there is a phase transition to a topological phase with an energy gap in the bulk and chiral Majorana fermions at the edge. However, recent nuclear magnetic resonance experiments suggest excitations without a gap in this phase, signalled by the cubic temperature dependence of the spin-lattice relaxation rate at low temperatures. In this work, I propose a mechanism to account for this experimental result. I use the localization of chiral Majorana modes in defects to explain the presence of gapless modes in the bulk. Treating the weak interaction between the chiral modes in the defects within a mean-field approximation, I find that these modes remain gapless when the interaction is below a critical value that depends on the magnetic field strength. I used the effective low-energy theory to calculate the spin-lattice relaxation rate and found a behavior that agrees with the experimental result.
We extend the scope of Kitaev spin liquids to non-Archimedean lattices. For the pentaheptite lattice, which results from the proliferation of Stone-Wales defects on the honeycomb lattice, we find an exactly solvable non-Abelian chiral spin liquid with spontaneous time-reversal symmetry breaking due to lattice loops of odd length. Our findings call for potential extensions of exact results for Kitaev models which are based on reflection positivity, which is not fulfilled by the pentaheptite lattice. We further elaborate on potential realizations of our chiral spin-liquid proposal in strained $\ensuremath{\alpha}\text{\ensuremath{-}}{\mathrm{RuCl}}_{3}$.
We study the effect of adding disorder to the Kitaev model on the hyperhoneycomb lattice, which hosts both gapped and gapless spin liquid phases with an emergent Z2{\mathbb{Z}}_{2}Z2​ gauge field. The latter has an unusual gapless spectrum of Majorana fermion excitations, with a co-dimension-two Fermi ring. We thus address the question of the interplay of topological physics and disorder by considering the properties of isolated single and pairs of vacancies. We show that near the vacancies, the local magnetic response to a field hz{h}_{z}hz​ is parametrically enhanced in comparison to the pristine bulk. Unlike the previously studied case of the 2D honeycomb Kitaev model, the vacancies do not bind a flux of the Z2{\mathbb{Z}}_{2}Z2​ gauge field. In the gapped phase, an isolated vacancy gives rise to effectively free spin-half moments with a nonuniversal coupling to an external field. In the gapless phase, the low-field magnetization is suppressed parametrically to ${(\ensuremath{-}ln{h}_{z})}^{\ensuremath{-}1/2}$ because of interactions with the surrounding spin liquid. We also show that a pair of vacancies is subject to a sublattice-dependent interaction on account of coupling through the bulk spin liquid, which is spatially anisotropic even when all Kitaev couplings have equal strength. This coupling is thus exponentially suppressed with distance in the gapped phase. In the gapless phase, two vacancies on the same (opposite) sublattice exhibit an enhanced (suppressed) low-field response, amounting to an effectively (anti-)ferromagnetic interaction.
In the Kitaev honeycomb model, a weak magnetic field gaps the gapless Majorana cone, driving the system into a gapped non-Abelian phase with Ising topological order. The edge supports a single chiral Majorana mode with chiral central charge c−=1/2c_- = 1/2c−​=1/2, yielding a half-quantized thermal Hall conductance κxy/T=π2kB2/6h\kappa_{xy}/T = \pi^2 k_B^2/6hκxy​/T=π2kB2​/6h. We rigorously investigate whether observing this half-quantized value uniquely identifies the non-Abelian Ising anyon sector, or whether Abelian topological orders or extrinsic mechanisms can produce the same signature. By combining the edge-bulk correspondence with the classification of strictly two-dimensional bosonic topological orders, we show that a chiral central charge c−=1/2c_-=1/2c−​=1/2 (mod 8) is the unique fingerprint of the Ising non-Abelian anyon theory among minimal bosonic topological orders. Abelian bosonic orders necessarily have integer c−c_-c−​, with the minimal nonzero value being c−=1c_-=1c−​=1. Thus, a robustly half-quantized κxy/T\kappa_{xy}/Tκxy​/T uniquely distinguishes the Majorana sector from Abelian alternatives, provided the system is a genuine 2D bosonic spin system free of invertible E8E_8E8​ stacking or phonon contamination. ## 1. Introduction The Kitaev honeycomb model is an exactly solvable model of a quantum spin liquid, characterized by fractionalized excitations known as anyons. In the absence of a magnetic field, the model hosts a gapless Majorana cone. A weak magnetic field in the [111] direction gaps this cone and induces a non-Abelian phase with Ising topological order. This phase supports a single chiral Majorana edge mode, which contributes to a quantized thermal Hall conductance. The central question addressed in this preprint is whether the observation of a half-quantized thermal Hall conductance, corresponding to a chiral central charge c−=1/2c_- = 1/2c−​=1/2, uniquely identifies the non-Abelian Ising anyon sector, or if Abelian topological orders can mimic this signature. ## 2. Background The thermal Hall conductance $\kappa_{x
Higher-order topological insulators are distinguished by the existence of topologically protected modes with codimension two or higher. Here, we report the manifestation of a second-order topological insulator in a two dimensional frustrated quantum magnet, which exhibits topological corner modes. Our exactly solvable model is a generalization of the Kitaev honeycomb model to the Shastry-Sutherland lattice that, besides a chiral spin liquid phase, exhibits a gapped spin liquid with Majorana corner modes, which are protected by two mirror symmetries. This second-order Kitaev spin liquid remains stable in the presence of thermal fluctuations and undergoes a finite-temperature phase transition evidenced in large-scale quantum Monte Carlo simulations.