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:1807.07926 · Physical review. B./Physical review. B

Thermally induced metallic phase in a gapped quantum spin liquid: Monte Carlo study of the Kitaev model with parity projection

Chris N. Self, Johannes Knolle, S. Iblisdir, Jiannis K. Pachos

Published Jan 25, 2019• 18 citations
arXivHTMLPDF

Abstract

Thermalization is a probabilistic process. As such, it is generally expected that when we increase the temperature of a system, its classical behavior dominates its quantum coherences. By employing the Gibbs state of a translationally invariant quantum spin liquid---Kitaev's honeycomb lattice model---we demonstrate that an insulating phase at $T=0$ becomes metallic purely by increasing temperature. In particular, we compute the finite-temperature distribution of energies and show that it diverges logarithmically, as we move to small energies. The corresponding wave functions become critical like at Anderson transitions. These characteristics are obtained within an exact Monte Carlo method that simulates the finite-temperature behavior of the Kitaev model. In particular, we take into account the projection onto the physical parity sectors, required for identifying the topological degeneracy of the model. Our work opens the possibility to detect thermal metal behavior in spin liquid experiments.

DOI
10.1103/physrevb.99.045142

Related papers

Finite-temperature phase transition to a Kitaev spin liquid phase on a hyperoctagon lattice: A large-scale quantum Monte Carlo study

Petr A. Mishchenko, Yasuyuki Kato, Yukitoshi Motome

The quantum spin liquid is an enigmatic quantum state in insulating magnets, in which conventional long-range order is suppressed by strong quantum fluctuations. Recently, an unconventional phase transition was reported between the low-temperature quantum spin liquid and the high-temperature paramagnet in the Kitaev model on a three-dimensional hyperhoneycomb lattice. Here, we show that a similar ``liquid-gas'' transition takes place in another three-dimensional lattice, the hyperoctagon lattice. We investigate the critical phenomena by adopting the Green-function based Monte Carlo technique with the kernel polynomial method, which enables systematic analysis of up to 2048 sites. The critical temperature is lower than that in the hyperhoneycomb case, reflecting the smaller flux gap. We also discuss the transition on the basis of an effective model in the anisotropic limit.

arXiv:1706.05057•Physical review. B./Physical review. B•Sep 15, 2017•22 citations

Thermodynamics of Kitaev Spin Liquids

Tim Eschmann

In the field of frustrated magnetism, Kitaev models provide prototypical examples of exactly solvable quantum spin liquids, in which the spin degrees of freedom fractionalize into Majorana fermions coupled to an emergent Z2 gauge field. While the ground states of these models are already well understood as exhibiting different kinds of Majorana (semi)metals, it has still been an open task to achieve a detailed understanding of the thermodynamics, and, namely, the low-temperature ordering of the gauge field into different Z2 flux configurations. In this thesis, we investigate the thermodynamics of Kitaev systems in two and three spatial dimensions with sign-problem-free quantum Monte Carlo simulations. In a first study of elementary 3D Kitaev models, we verify that the ground state Z2 flux sectors of these systems are entirely determined by their elementary plaquette length – a result which shows the validity of Lieb’s theorem for lattice geometries which lack the geometric requirements for its proof. We closely investigate the low-temperature phase transition associated with gauge-ordering, which is a particular realization of an inverted Ising phase transition, as it occurs in general lattice Z2 gauge theories. Our results corroborate the understanding of this transition as separating different regimes in terms of vison-loop excitations, by showing a clear correlation between the critical temperature and the vison gap. We also introduce the concept of “gauge frustration”, which, for a particular 3D Kitaev model, leads to the suppression of the phase transition and a more complex physical behavior at low temperatures. A second quantum Monte Carlo study focuses on a generalized 2D Kitaev model on a five-coordinated lattice system. Here, the gauge ordering is accompanied by the spontaneous breaking of time-reversal symmetry, a scenario which not only allows for a variety of topological ground states, but also for the occurrence of a phase transition in two spatial dimensions. We show that this model exhibits such a transition at a particularly high temperature scale. Moreover, the system possesses a number of phases where the Z2 fluxes are only partially ordered.

•Jul 27, 2020•1 citation

Heat transport in the anisotropic Kitaev spin liquid

Angelo Pidatella, Alexandros Metavitsiadis, Wolfram Brenig

We present a study of longitudinal thermal transport in the Kitaev spin model on the honeycomb lattice, focusing on the role of anisotropic exchange to cover both gapless and gapped phases. Employing a complementary combination of exact diagonalization on small systems and an average gauge configuration approach for up to $\ensuremath{\sim}O({10}^{4})$ spinful sites, we report results for the dynamical energy current autocorrelation function as well as the dc thermal conductivity over a wide range of temperatures and exchange anisotropies. Despite a pseudogap in the current correlation spectra, induced by emergent thermal gauge disorder on any finite system, we find that in the thermodynamic limit, gapless and gapful phases both feature normal dissipative transport, with a temperature dependence crossing over from power law to exponentially activated behavior upon gap opening.

arXiv:1810.04674•Physical review. B./Physical review. B•Feb 20, 2019•19 citations

Low-energy Majorana states in spin liquid transitions in a three-dimensional Kitaev model

Joji Nasu, Masafumi Udagawa, Yukitoshi Motome

A three-dimensional Kitaev model on a hyperhoneycomb lattice is investigated numerically at finite temperature. The Kitaev model is one of the solvable quantum spin models, where the ground state is given by gapped and gapless spin liquids, depending on the anisotropy of the interactions. This model can be rewritten as a free Majorana fermion system coupled with Z 2 variables. The density of states of Majorana fermions shows an excitation gap in the gapped region, while it is semimetallic in the gapless region reflecting the Dirac node. Performing the Monte Carlo simulation, we calculate the temperature dependence of the Majorana spectra. We find that the semimetallic dip is filled as temperature increases in the gapless region, but surprisingly, the spectrum develops an excitation gap in the region near the gapless-gapped boundary. Such changes of the low-energy spectrum appear sharply at the transition temperature from the spin liquid to the paramagnetic state. The results indicate that thermal fluctuations of the Z 2 fields significantly influence the low-energy state of Majorana fermions, especially in the spin liquid formation.

arXiv:1409.4865•Journal of Physics Conference Series•Mar 18, 2015•8 citations

Spin-S Decorated Honeycomb Kitaev Model with S ≥ 1

Tomonari Mizoguchi

In the prior work [J. Phys. Soc. Jpn. 91 , 124709 (2022)], we have introduced the spin-half decorated honeycomb Kitaev model, and have elucidated its exactly-solvable nature at any temperature. In this work, we extend the model to that with an arbitrary spin quantum number S . We show that the ground state is classical spin liquid whose degeneracy is independent of S . As for the fi nite-temperature properties, the partition function cannot be obtained analytically, unlike the spin-half case. We therefore perform the Monte Carlo simulation to reveal the fi nite-temperature properties, taking S = 1 and 3/2 cases as examples. We fi nd that the temperature dependence of the energy and the specific heat exhibits typical behaviors of the classical spin liquid. In particular, the broad peak of the specific heat is accounted for by the configuration of the classical variables on the edge of the hexagons.

•Nov 5, 2024•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
Thermalization is a probabilistic process. As such, it is generally expected that when we increase the temperature of a system, its classical behavior dominates its quantum coherences. By employing the Gibbs state of a translationally invariant quantum spin liquid---Kitaev's honeycomb lattice model---we demonstrate that an insulating phase at T=0T=0T=0 becomes metallic purely by increasing temperature. In particular, we compute the finite-temperature distribution of energies and show that it diverges logarithmically, as we move to small energies. The corresponding wave functions become critical like at Anderson transitions. These characteristics are obtained within an exact Monte Carlo method that simulates the finite-temperature behavior of the Kitaev model. In particular, we take into account the projection onto the physical parity sectors, required for identifying the topological degeneracy of the model. Our work opens the possibility to detect thermal metal behavior in spin liquid experiments.
The quantum spin liquid is an enigmatic quantum state in insulating magnets, in which conventional long-range order is suppressed by strong quantum fluctuations. Recently, an unconventional phase transition was reported between the low-temperature quantum spin liquid and the high-temperature paramagnet in the Kitaev model on a three-dimensional hyperhoneycomb lattice. Here, we show that a similar ``liquid-gas'' transition takes place in another three-dimensional lattice, the hyperoctagon lattice. We investigate the critical phenomena by adopting the Green-function based Monte Carlo technique with the kernel polynomial method, which enables systematic analysis of up to 2048 sites. The critical temperature is lower than that in the hyperhoneycomb case, reflecting the smaller flux gap. We also discuss the transition on the basis of an effective model in the anisotropic limit.
In the field of frustrated magnetism, Kitaev models provide prototypical examples of exactly solvable quantum spin liquids, in which the spin degrees of freedom fractionalize into Majorana fermions coupled to an emergent Z2 gauge field. While the ground states of these models are already well understood as exhibiting different kinds of Majorana (semi)metals, it has still been an open task to achieve a detailed understanding of the thermodynamics, and, namely, the low-temperature ordering of the gauge field into different Z2 flux configurations. In this thesis, we investigate the thermodynamics of Kitaev systems in two and three spatial dimensions with sign-problem-free quantum Monte Carlo simulations. In a first study of elementary 3D Kitaev models, we verify that the ground state Z2 flux sectors of these systems are entirely determined by their elementary plaquette length – a result which shows the validity of Lieb’s theorem for lattice geometries which lack the geometric requirements for its proof. We closely investigate the low-temperature phase transition associated with gauge-ordering, which is a particular realization of an inverted Ising phase transition, as it occurs in general lattice Z2 gauge theories. Our results corroborate the understanding of this transition as separating different regimes in terms of vison-loop excitations, by showing a clear correlation between the critical temperature and the vison gap. We also introduce the concept of “gauge frustration”, which, for a particular 3D Kitaev model, leads to the suppression of the phase transition and a more complex physical behavior at low temperatures. A second quantum Monte Carlo study focuses on a generalized 2D Kitaev model on a five-coordinated lattice system. Here, the gauge ordering is accompanied by the spontaneous breaking of time-reversal symmetry, a scenario which not only allows for a variety of topological ground states, but also for the occurrence of a phase transition in two spatial dimensions. We show that this model exhibits such a transition at a particularly high temperature scale. Moreover, the system possesses a number of phases where the Z2 fluxes are only partially ordered.
We present a study of longitudinal thermal transport in the Kitaev spin model on the honeycomb lattice, focusing on the role of anisotropic exchange to cover both gapless and gapped phases. Employing a complementary combination of exact diagonalization on small systems and an average gauge configuration approach for up to $\ensuremath{\sim}O({10}^{4})$ spinful sites, we report results for the dynamical energy current autocorrelation function as well as the dc thermal conductivity over a wide range of temperatures and exchange anisotropies. Despite a pseudogap in the current correlation spectra, induced by emergent thermal gauge disorder on any finite system, we find that in the thermodynamic limit, gapless and gapful phases both feature normal dissipative transport, with a temperature dependence crossing over from power law to exponentially activated behavior upon gap opening.
A three-dimensional Kitaev model on a hyperhoneycomb lattice is investigated numerically at finite temperature. The Kitaev model is one of the solvable quantum spin models, where the ground state is given by gapped and gapless spin liquids, depending on the anisotropy of the interactions. This model can be rewritten as a free Majorana fermion system coupled with Z 2 variables. The density of states of Majorana fermions shows an excitation gap in the gapped region, while it is semimetallic in the gapless region reflecting the Dirac node. Performing the Monte Carlo simulation, we calculate the temperature dependence of the Majorana spectra. We find that the semimetallic dip is filled as temperature increases in the gapless region, but surprisingly, the spectrum develops an excitation gap in the region near the gapless-gapped boundary. Such changes of the low-energy spectrum appear sharply at the transition temperature from the spin liquid to the paramagnetic state. The results indicate that thermal fluctuations of the Z 2 fields significantly influence the low-energy state of Majorana fermions, especially in the spin liquid formation.
In the prior work [J. Phys. Soc. Jpn. 91 , 124709 (2022)], we have introduced the spin-half decorated honeycomb Kitaev model, and have elucidated its exactly-solvable nature at any temperature. In this work, we extend the model to that with an arbitrary spin quantum number S . We show that the ground state is classical spin liquid whose degeneracy is independent of S . As for the fi nite-temperature properties, the partition function cannot be obtained analytically, unlike the spin-half case. We therefore perform the Monte Carlo simulation to reveal the fi nite-temperature properties, taking S = 1 and 3/2 cases as examples. We fi nd that the temperature dependence of the energy and the specific heat exhibits typical behaviors of the classical spin liquid. In particular, the broad peak of the specific heat is accounted for by the configuration of the classical variables on the edge of the hexagons.
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.