The Kitaev model exhibits a quantum spin liquid hosting emergent fractionalized excitations. We study the Kitaev model on the honeycomb lattice coupled to a magnetic field along the [111] axis. Utilizing large-scale matrix product-based numerical models, we confirm three phases with transitions at different field strengths depending on the sign of the Kitaev exchange: a non-Abelian topological phase at low fields, an enigmatic intermediate regime only present for antiferromagnetic Kitaev exchange, and a field-polarized phase. For the topological phase, we numerically observe the expected cubic scaling of the gap and extract the quantum dimension of the non-Abelian anyons. Furthermore, we investigate dynamical signatures of the topological and the field-polarized phase using a matrix product operator-based time evolution method.The Kitaev model exhibits a quantum spin liquid hosting emergent fractionalized excitations. We study the Kitaev model on the honeycomb lattice coupled to a magnetic field along the [111] axis. Utilizing large-scale matrix product-based numerical models, we confirm three phases with transitions at different field strengths depending on the sign of the Kitaev exchange: a non-Abelian topological phase at low fields, an enigmatic intermediate regime only present for antiferromagnetic Kitaev exchange, and a field-polarized phase. For the topological phase, we numerically observe the expected cubic scaling of the gap and extract the quantum dimension of the non-Abelian anyons. Furthermore, we investigate dynamical signatures of the topological and the field-polarized phase using a matrix product operator-based time evolution method.

arXiv:1804.06811Physical review. B./Physical review. BJul 17, 2018116 citations

Spin Transport in the Quantum Spin Liquid State in the S = 1 Kitaev Model: Role of the Fractionalized Quasiparticles

Akihisa Koga, Tetsuya Minakawa, Yuta Murakami +1 more

We investigate the real-time spin response of the $S=1$ Kitaev model upon stimuli of a pulsed magnetic field in one of the edges using the exact diagonalization method. It is found that the pulsed magnetic field has no effect on the appearance of the spin moments in the quantum spin liquid region, but induces the spin oscillations in the other edge region with a small magnetic field. This is understood by the existence of the itinerant quasiparticles, which carry the spin excitations without the spin polarization in the quantum spin liquid state. This suggests that the spin fractionalizations occur in the $S=1$ Kitaev model as well as the exactly solvable $S=1/2$ Kitaev one and the fractionalized quasiparticles play an essential role in the spin transport.We investigate the real-time spin response of the $S=1$ Kitaev model upon stimuli of a pulsed magnetic field in one of the edges using the exact diagonalization method. It is found that the pulsed magnetic field has no effect on the appearance of the spin moments in the quantum spin liquid region, but induces the spin oscillations in the other edge region with a small magnetic field. This is understood by the existence of the itinerant quasiparticles, which carry the spin excitations without the spin polarization in the quantum spin liquid state. This suggests that the spin fractionalizations occur in the $S=1$ Kitaev model as well as the exactly solvable $S=1/2$ Kitaev one and the fractionalized quasiparticles play an essential role in the spin transport.

arXiv:2001.07344Journal of the Physical Society of JapanFeb 12, 202016 citations

Dynamical and Topological Signatures of the Kitaev-Model in a [111] Magnetic Field

Matthias Gohlke, Roderich Moessner, Frank Pollmann

Bulletin of the American Physical SocietyMar 4, 20190 citations

Phonon dynamics in the site-disordered Kitaev spin liquid

Vitor Dantas, Wen-Han Kao, Natalia Borisovna Perkins

The Kitaev honeycomb model provides a paradigmatic example of an exactly solvable quantum spin liquid (QSL), where spins fractionalize into itinerant Majorana fermions coupled to a static background of ${\mathbb{Z}}_{2}$ gauge fluxes. This model has attracted significant interest due to its potential experimental realization in spin-orbit Mott insulators like $\ensuremath{\alpha}\text{\ensuremath{-}}{\mathrm{RuCl}}_{3}$. Among various experimental techniques, ultrasound measurements of sound attenuation have emerged as a promising approach to detect spin fractionalization in these materials. However, deviations from the ideal Kitaev model, often due to disorder, introduce localized modes that dominate the low-energy physics. To investigate these effects, we calculate the sound attenuation coefficient in the site-disordered Kitaev honeycomb model under an applied magnetic field that breaks time-reversal symmetry. Our analysis reveals that quasilocalized modes from quasivacancies impact the phonon self-energy, yet the sound attenuation coefficient maintains its sixfold symmetry and linear temperature dependence at low temperatures, even with disorder. This robustness underscores sound attenuation's reliability as a probe for spin fractionalization. Furthermore, we show that this linear behavior persists under an external field and in the random-flux sector, highlighting the persistent influence of fractionalized excitations, despite disorder.The Kitaev honeycomb model provides a paradigmatic example of an exactly solvable quantum spin liquid (QSL), where spins fractionalize into itinerant Majorana fermions coupled to a static background of ${\mathbb{Z}}_{2}$ gauge fluxes. This model has attracted significant interest due to its potential experimental realization in spin-orbit Mott insulators like $\ensuremath{\alpha}\text{\ensuremath{-}}{\mathrm{RuCl}}_{3}$. Among various experimental techniques, ultrasound measurements of sound attenuation have emerged as a promising approach to detect spin fractionalization in these materials. However, deviations from the ideal Kitaev model, often due to disorder, introduce localized modes that dominate the low-energy physics. To investigate these effects, we calculate the sound attenuation coefficient in the site-disordered Kitaev honeycomb model under an applied magnetic field that breaks time-reversal symmetry. Our analysis reveals that quasilocalized modes from quasivacancies impact the phonon self-energy, yet the sound attenuation coefficient maintains its sixfold symmetry and linear temperature dependence at low temperatures, even with disorder. This robustness underscores sound attenuation's reliability as a probe for spin fractionalization. Furthermore, we show that this linear behavior persists under an external field and in the random-flux sector, highlighting the persistent influence of fractionalized excitations, despite disorder.

arXiv:2406.19140Physical review. B./Physical review. BSep 23, 20245 citations

Thermal transport in the Kitaev model

譲治那須, Joji Nasu, 幸年求 +2 more

Feb 1, 20170 citations

We investigate the real-time spin response of the

S=1

Kitaev model upon stimuli of a pulsed magnetic field in one of the edges using the exact diagonalization method. It is found that the pulsed magnetic field has no effect on the appearance of the spin moments in the quantum spin liquid region, but induces the spin oscillations in the other edge region with a small magnetic field. This is understood by the existence of the itinerant quasiparticles, which carry the spin excitations without the spin polarization in the quantum spin liquid state. This suggests that the spin fractionalizations occur in the

S=1

Kitaev model as well as the exactly solvable

S=1/2

Kitaev one and the fractionalized quasiparticles play an essential role in the spin transport.

{\mathbb{Z}}_{2}

gauge fluxes. This model has attracted significant interest due to its potential experimental realization in spin-orbit Mott insulators like $\ensuremath{\alpha}\text{\ensuremath{-}}{\mathrm{RuCl}}_{3}$. Among various experimental techniques, ultrasound measurements of sound attenuation have emerged as a promising approach to detect spin fractionalization in these materials. However, deviations from the ideal Kitaev model, often due to disorder, introduce localized modes that dominate the low-energy physics. To investigate these effects, we calculate the sound attenuation coefficient in the site-disordered Kitaev honeycomb model under an applied magnetic field that breaks time-reversal symmetry. Our analysis reveals that quasilocalized modes from quasivacancies impact the phonon self-energy, yet the sound attenuation coefficient maintains its sixfold symmetry and linear temperature dependence at low temperatures, even with disorder. This robustness underscores sound attenuation's reliability as a probe for spin fractionalization. Furthermore, we show that this linear behavior persists under an external field and in the random-flux sector, highlighting the persistent influence of fractionalized excitations, despite disorder.