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:2101.05959 · Physical Review Research

Topological nematic phase transition in Kitaev magnets under applied magnetic fields

Masahiro O. Takahashi, Masahiko G. Yamada, Daichi Takikawa, Takeshi Mizushima, Satoshi Fujimoto

Published Jun 7, 2021• 12 citations
arXivHTMLPDF

Abstract

We propose a scenario of realizing the toric code phase, which can be potentially utilized for fault-tolerant quantum computation, in candidate materials of Kitaev magnets.It is demonstrated that four-body interactions among Majorana fermions in the Kitaev spin liquid state, which are induced by applied magnetic fields as well as non-Kitaev-type exchange interactions, trigger a nematic phase transition of Majorana bonds without magnetic orders, accompanying the change of the Chern number from ±1 to zero.This gapful spin liquid state with zero Chern number is simply the toric code phase.Our result potentially explains the topological nematic transition recently observed in α-RuCl 3 via heat capacity measurements (O.Tanaka et al.,

DOI
10.1103/physrevresearch.3.023189

Related papers

Electric Probe for the Toric Code Phase in Kitaev Materials through the Hyperfine Interaction

Masahiko G. Yamada, Satoshi Fujimoto

The Kitaev model is a remarkable spin model with gapped and gapless spin liquid phases, which are potentially realized in iridates and α-RuCl_{3}. In the recent experiment of α-RuCl_{3}, the signature of a nematic transition to the gapped toric code phase, which breaks the C_{3} symmetry of the system, has been observed through the angle dependence of the heat capacity. We here propose a mechanism by which the nematic transition can be detected electrically. This is seemingly impossible because J_{eff}=1/2 spins do not have an electric quadrupole moment (EQM). However, in the second-order perturbation, the virtual state with a nonzero EQM appears, which makes the nematic order parameter detectable by nuclear magnetic resonance and Mössbauer spectroscopy. The purely magnetic origin of the EQM is different from conventional electronic nematic phases, allowing the direct detection of the realization of Kitaev's toric error-correction code.

arXiv:2012.08825•Physical Review Letters•Jul 19, 2021•5 citations

Topological phase transition to Abelian anyon phases due to off-diagonal exchange interaction in the Kitaev spin liquid state

Daichi Takikawa, Satoshi Fujimoto

We investigate how the Kitaev spin liquid state described by Majorana fermions coupled with ${Z}_{2}$ gauge fields is affected by non-Kitaev interactions which exist in real candidate materials of the Kitaev magnet. It is found that the off-diagonal exchange interaction referred to as the ${\mathrm{\ensuremath{\Gamma}}}^{\ensuremath{'}}$ term dramatically changes the Majorana band structure in the case of the antiferromagnetic Kitaev interaction and gives rise to a topological phase transition from a non-Abelian topological phase with the Chern number equal to $\ifmmode\pm\else\textpm\fi{}1$ to an Abelian phase with the Chern number equal to $\ifmmode\pm\else\textpm\fi{}2$, in which the ${Z}_{2}$ vortices behave as Abelian anyons. On the other hand, other non-Kitaev interactions such as the Heisenberg interaction and the $\mathrm{\ensuremath{\Gamma}}$ term only affect the bandwidth of the Majorana band as long as the spin liquid state is not destabilized.

arXiv:2003.05645•Physical review. B./Physical review. B•Nov 9, 2020•17 citations

Successive Majorana topological transitions driven by a magnetic field in the Kitaev model

Joji Nasu, Yasuyuki Kato, Yoshitomo Kamiya +1 more

We study quantum phase transitions in the honeycomb Kitaev model under a magnetic field, focusing on the topological nature of Majorana fermion excitations. We find a gapless phase between the low-field gapless quantum spin liquid and the high-field gapped forced-ferromagnetic state for the antiferromagnetic Kitaev model in the [001] field by using the Majorana mean-field theory, in conjunction with the exact diagonalization and the spin-wave theory supporting the validity of this approach. The transition between the two gapless phases is driven by a topological change of the Majorana spectrum---line node formation interconnecting two Majorana cones. The peculiar change of the Majorana band topology is rationalized by a sign change of the effective Kitaev coupling by the magnetic field, which does not occur in the ferromagnetic Kitaev case. Upon tilting the magnetic field away from [001], the two gapless phases become gapped and topologically nontrivial, characterized by nonzero Chern numbers with different signs. The sign change of the Chern number leads to a reversal of the thermal edge current in the half-quantized thermal Hall effect.

arXiv:1805.02423•Physical review. B./Physical review. B•Aug 30, 2018•72 citations

Mixed-State Topological Transition and Emergent Fractionalized Supersymmetry in the Non-Abelian Kitaev Spin Liquid

Zhou-Quan Wan, Hong Yao, Shao-Kai Jian

We study a mixed-state topological transition in the non-Abelian Kitaev spin liquid driven by a bond-dephasing channel. In the vectorized picture, bond dephasing maps onto interactions between two time-reversed fractionalized Majorana systems coupled to gapped $\mathbb Z_2$ gauge fields, enabling sign-problem-free Monte Carlo simulations. We show that increasing dephasing condenses an inter-copy fermion pair, converting ${\rm Ising}\boxtimes\overline{\rm{Ising}}$ to toric-code order in the Choi state and yielding intrinsically mixed-state topological order upon unfolding. More interestingly, at a temporal interface between topological and trivial Kitaev states, a Chern-number mismatch enforces a gapless Majorana mode. Dephasing then drives a mixed-state topological transition at which the gapless mode develops emergent $\mathcal N=1$ supersymmetry. Our Monte Carlo simulations yield $ν=1.27(3)$ and $η_b\simeqη_f\simeq0.40$, consistent with the exact supersymmetric values $5/4$ and $2/5$. The supersymmetric partners are fractionalized and appear physically as distinct gauge-invariant spin strings, providing concrete observables for future experiments.

cond-mat.str-elCross-listedarXiv:2610.38741•Oct 30, 2026•0 citations

Magnetic field induced topological transitions and thermal conductivity in a generalized Kitaev model

Heqiu Li, Yong Baek Kim, Hae‐Young Kee

Recent experiments on Kitaev spin liquid candidate materials reported nonmonotonic behavior of thermal conductivity as a function of magnetic field, which lead to conflicting interpretations of its origin. Motivated by this development, we study the magnetic field dependence of thermal conductivity of a generalized Kitaev model, which allows the phase transitions between different flux sectors as a function of the magnetic field. The thermal conductivity due to Majorana fermions shows dip-bump structures as the magnetic field increases, which is caused by either the transitions between different flux sectors of Kitaev spin liquids or the topological transitions that change the Majorana Chern number within the same flux sector. It is shown that the change of Chern number is closely related to the four-Majorana-fermion interaction induced by the magnetic field. The nonmonotonic behavior in thermal conductivity emerges at finite temperature, and it becomes weaker when temperature decreases toward zero. Our model provides a generic mechanism for the Kitaev spin liquids to develop nonmonotonic magnetic-field dependence of thermal conductivity while the comparison to realistic materials remains an open question for future investigation.

arXiv:2202.12315•Physical review. B./Physical review. B•Jun 27, 2022•7 citations

Quantum liquid crystals in the finite-field K$Γ$ model for $α$-RuCl$_3$

Masahiko G. Yamada, Satoshi Fujimoto

We study the extended Kitaev model called the K$Γ$ model, using a perturbative expansion combined with a well-controlled mean-field approximation and a cutting-edge exact diagonalization. In the phase diagram, we discover a nematic Kitaev spin liquid and a Kekulé Kitaev spin liquid. The former potentially explains the high-field nematic state with zero Chern number experimentally observed in $α$-RuCl$_3$, even for sufficiently small values of $Γ/|K|$. The latter has a Majorana zero mode in its $Z_3$ vortex core, which can be potentially controlled by the domain wall motion. This opens a possible application of the quantum liquid crystal phases in the K$Γ$ model to the topological quantum computation.

arXiv:2107.03045•Jul 7, 2021•1 citation
We propose a scenario of realizing the toric code phase, which can be potentially utilized for fault-tolerant quantum computation, in candidate materials of Kitaev magnets.It is demonstrated that four-body interactions among Majorana fermions in the Kitaev spin liquid state, which are induced by applied magnetic fields as well as non-Kitaev-type exchange interactions, trigger a nematic phase transition of Majorana bonds without magnetic orders, accompanying the change of the Chern number from ±1 to zero.This gapful spin liquid state with zero Chern number is simply the toric code phase.Our result potentially explains the topological nematic transition recently observed in α-RuCl 3 via heat capacity measurements (O.Tanaka et al.,
The Kitaev model is a remarkable spin model with gapped and gapless spin liquid phases, which are potentially realized in iridates and α-RuCl_{3}. In the recent experiment of α-RuCl_{3}, the signature of a nematic transition to the gapped toric code phase, which breaks the C_{3} symmetry of the system, has been observed through the angle dependence of the heat capacity. We here propose a mechanism by which the nematic transition can be detected electrically. This is seemingly impossible because J_{eff}=1/2 spins do not have an electric quadrupole moment (EQM). However, in the second-order perturbation, the virtual state with a nonzero EQM appears, which makes the nematic order parameter detectable by nuclear magnetic resonance and Mössbauer spectroscopy. The purely magnetic origin of the EQM is different from conventional electronic nematic phases, allowing the direct detection of the realization of Kitaev's toric error-correction code.
We investigate how the Kitaev spin liquid state described by Majorana fermions coupled with Z2{Z}_{2}Z2​ gauge fields is affected by non-Kitaev interactions which exist in real candidate materials of the Kitaev magnet. It is found that the off-diagonal exchange interaction referred to as the ${\mathrm{\ensuremath{\Gamma}}}^{\ensuremath{'}}$ term dramatically changes the Majorana band structure in the case of the antiferromagnetic Kitaev interaction and gives rise to a topological phase transition from a non-Abelian topological phase with the Chern number equal to $\ifmmode\pm\else\textpm\fi{}1$ to an Abelian phase with the Chern number equal to $\ifmmode\pm\else\textpm\fi{}2$, in which the Z2{Z}_{2}Z2​ vortices behave as Abelian anyons. On the other hand, other non-Kitaev interactions such as the Heisenberg interaction and the $\mathrm{\ensuremath{\Gamma}}$ term only affect the bandwidth of the Majorana band as long as the spin liquid state is not destabilized.
We study quantum phase transitions in the honeycomb Kitaev model under a magnetic field, focusing on the topological nature of Majorana fermion excitations. We find a gapless phase between the low-field gapless quantum spin liquid and the high-field gapped forced-ferromagnetic state for the antiferromagnetic Kitaev model in the [001] field by using the Majorana mean-field theory, in conjunction with the exact diagonalization and the spin-wave theory supporting the validity of this approach. The transition between the two gapless phases is driven by a topological change of the Majorana spectrum---line node formation interconnecting two Majorana cones. The peculiar change of the Majorana band topology is rationalized by a sign change of the effective Kitaev coupling by the magnetic field, which does not occur in the ferromagnetic Kitaev case. Upon tilting the magnetic field away from [001], the two gapless phases become gapped and topologically nontrivial, characterized by nonzero Chern numbers with different signs. The sign change of the Chern number leads to a reversal of the thermal edge current in the half-quantized thermal Hall effect.
We study a mixed-state topological transition in the non-Abelian Kitaev spin liquid driven by a bond-dephasing channel. In the vectorized picture, bond dephasing maps onto interactions between two time-reversed fractionalized Majorana systems coupled to gapped Z2\mathbb Z_2Z2​ gauge fields, enabling sign-problem-free Monte Carlo simulations. We show that increasing dephasing condenses an inter-copy fermion pair, converting Ising⊠Ising‾{\rm Ising}\boxtimes\overline{\rm{Ising}}Ising⊠Ising​ to toric-code order in the Choi state and yielding intrinsically mixed-state topological order upon unfolding. More interestingly, at a temporal interface between topological and trivial Kitaev states, a Chern-number mismatch enforces a gapless Majorana mode. Dephasing then drives a mixed-state topological transition at which the gapless mode develops emergent N=1\mathcal N=1N=1 supersymmetry. Our Monte Carlo simulations yield ν=1.27(3)ν=1.27(3)ν=1.27(3) and ηb≃ηf≃0.40η_b\simeqη_f\simeq0.40ηb​≃ηf​≃0.40, consistent with the exact supersymmetric values 5/45/45/4 and 2/52/52/5. The supersymmetric partners are fractionalized and appear physically as distinct gauge-invariant spin strings, providing concrete observables for future experiments.
Recent experiments on Kitaev spin liquid candidate materials reported nonmonotonic behavior of thermal conductivity as a function of magnetic field, which lead to conflicting interpretations of its origin. Motivated by this development, we study the magnetic field dependence of thermal conductivity of a generalized Kitaev model, which allows the phase transitions between different flux sectors as a function of the magnetic field. The thermal conductivity due to Majorana fermions shows dip-bump structures as the magnetic field increases, which is caused by either the transitions between different flux sectors of Kitaev spin liquids or the topological transitions that change the Majorana Chern number within the same flux sector. It is shown that the change of Chern number is closely related to the four-Majorana-fermion interaction induced by the magnetic field. The nonmonotonic behavior in thermal conductivity emerges at finite temperature, and it becomes weaker when temperature decreases toward zero. Our model provides a generic mechanism for the Kitaev spin liquids to develop nonmonotonic magnetic-field dependence of thermal conductivity while the comparison to realistic materials remains an open question for future investigation.
Quantum liquid crystals in the finite-field KΓΓΓ model for ααα-RuCl3_33​
We study the extended Kitaev model called the KΓΓΓ model, using a perturbative expansion combined with a well-controlled mean-field approximation and a cutting-edge exact diagonalization. In the phase diagram, we discover a nematic Kitaev spin liquid and a Kekulé Kitaev spin liquid. The former potentially explains the high-field nematic state with zero Chern number experimentally observed in ααα-RuCl3_33​, even for sufficiently small values of Γ/∣K∣Γ/|K|Γ/∣K∣. The latter has a Majorana zero mode in its Z3Z_3Z3​ vortex core, which can be potentially controlled by the domain wall motion. This opens a possible application of the quantum liquid crystal phases in the KΓΓΓ model to the topological quantum computation.