Incarnation of Majorana Fermions in Kitaev Quantum Spin Lattice

Do, Seung-Hwan; Park, Sang‐Youn; Yoshitake, Junki; Nasu, Joji; Motome, Yukitoshi; Kwon, Yong Seung; Adroja, D. T.; Voneshen, David; Kim, Kyoo; Jang, Tae-Hwan; Park, J. H.; Choi, Kwang‐Yong; Ji, Sungdae

doi:10.48550/arxiv.1703.01081

Cited by 10 publications

(36 citation statements)

References 21 publications

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“…Also in the ground state, the dynamical spin structure factor S(q, ω) shows a gap due to the flux excitation and strong incoherent spectra from the composite excitations between itinerant Majorana fermions and localized gauge fluxes [11]. Such incoherent spectra were indeed observed in recent inelestic neutron scattering experiments for a candidate for the Kitaev QSL, α-RuCl 3 [12,13]. The magnetic Raman scattering spectra also shows a broad continuum dominated by the itinerant Majorana fermions, in marked contrast to conventional insulating magnets [14].…”

Section: Introductionmentioning

confidence: 54%

Majorana dynamical mean-field study of spin dynamics at finite temperatures in the honeycomb Kitaev model

et al. 2017

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A prominent feature of quantum spin liquids is fractionalization of the spin degree of freedom. Fractionalized excitations have their own dynamics in different energy scales, and hence, affect finite-temperature (T ) properties in a peculiar manner even in the paramagnetic state harboring the quantum spin liquid state. We here present a comprehensive theoretical study of the spin dynamics in a wide T range for the Kitaev model on a honeycomb lattice, whose ground state is such a quantum spin liquid. In this model, the fractionalization occurs to break up quantum spins into itinerant matter fermions and localized gauge fluxes, which results in two crossovers at very different T scales. Extending the previous study for the isotropic coupling case [J. Yoshitake, J. Nasu, and Y. Motome, Phys. Rev. Lett. 117, 157203 (2016)], we calculate the dynamical spin structure factor S(q, ω), the NMR relaxation rate 1/T1, and the magnetic susceptibility χ while changing the anisotropy in the exchange coupling constants, by using the dynamical mean-field theory based on a Majorana fermion representation. We describe the details of the methodology including the continuous-time quantum Monte Carlo method for computing dynamical spin correlations and the maximum entropy method for analytic continuation. We confirm that the combined method provides accurate results in a wide T range including the region where the spins are fractionalized. We find that also in the anisotropic cases the system exhibits peculiar behaviors below the high-T crossover whose temperature is comparable to the average of the exchange constants: S(q, ω) shows an inelastic response at the energy scale of the averaged exchange constant, 1/T1 continues to grow even though the equal-time spin correlations are saturated and almost T independent, and χ deviates from the Curie-Weiss behavior. In particular, when the exchange interaction in one direction is stronger than the other two, the dynamical quantities exhibit qualitatively different T dependences from the isotropic case at low T , reflecting the opposite parity between the flux-free ground state and the flux-excited state, and a larger energy cost for flipping a spin in the strong interaction direction. On the other hand, when the exchange anisotropy is in the opposite way, the results are qualitatively similar to those in the isotropic case. All these behaviors manifest the spin fractionalization in the paramagnetic region. Among them, the dichotomy between the static and dynamical spin correlations is unusual behavior hardly seen in conventional magnets. We discuss the relation between the dichotomy and the spatial configuration of gauge fluxes. Our results could stimulate further experimental and theoretical analyses of candidate materials for the Kitaev quantum spin liquids.

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Section: Introductionmentioning

confidence: 54%

Majorana dynamical mean-field study of spin dynamics at finite temperatures in the honeycomb Kitaev model

et al. 2017

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“…Currently, α-RuCl 3 stands as the most promising candidate for the realization of the Kitaev QSL [13,[18][19][20][21]. Among the listed signatures, a spin-excitation continuum was observed by Raman spectroscopy [13,18] and inelastic neutron scattering [19][20][21], and the two-step thermal fractionalization was confirmed by specific-heat measurements [21], all in zero field. However, an application of a finite field, which should affect the gaps of both types of quasiparticles differently, is crucial to identify them.…”

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confidence: 93%

“…And third, in the presence of an external magnetic field, the Majorana fermions also acquire a gap, which is predicted to grow with the characteristic third power of the field in the low-field region [6,16,17]. Currently, α-RuCl 3 stands as the most promising candidate for the realization of the Kitaev QSL [13,[18][19][20][21]. Among the listed signatures, a spin-excitation continuum was observed by Raman spectroscopy [13,18] and inelastic neutron scattering [19][20][21], and the two-step thermal fractionalization was confirmed by specific-heat measurements [21], all in zero field.…”

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confidence: 99%

Observation of two types of fractional excitation in the Kitaev honeycomb magnet

et al. 2018

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Quantum spin liquid is a disordered magnetic state with fractional spin excitations. Its clearest example is found in an exactly solved Kitaev honeycomb model where a spin flip fractionalizes into two types of anyons, quasiparticles that are neither fermions nor bosons: a pair of gauge fluxes and a Majorana fermion. Here we demonstrate this kind of fractionalization in the Kitaev paramagnetic state of the honeycomb magnet α-RuCl3. The spin-excitation gap measured by nuclear magnetic resonance consists of the predicted Majorana fermion contribution following the cube of the applied magnetic field, and a finite zero-field contribution matching the predicted size of the gauge-flux gap. The observed fractionalization into gapped anyons survives in a broad range of temperatures and magnetic fields despite inevitable non-Kitaev interactions between the spins, which are predicted to drive the system towards a gapless ground state. The gapped character of both anyons is crucial for their potential application in topological quantum computing.

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“…Recently, many candidates have been explored in both quasi-2D and 3D materials [22][23][24][25][26]. Some indications of the fractionalization were observed, for instance, in the specific heat [27], magnetic Raman scattering [28,29], inelastic neutron scattering [30][31][32], and thermal transport [33,34]. However, such indications are for rather high-T features, corresponding to the theoretical predictions around and below T H associated with itinerant matter fermions [17-19, 35, 36].…”

Section: Introductionmentioning

confidence: 99%

Temperature evolution of spin dynamics in two- and three-dimensional Kitaev models: Influence of fluctuating Z2 flux

2017

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The long-sought quantum spin liquid is a quantum-entangled magnetic state leading to the fractionalization of spin degrees of freedom. Quasiparticles emergent from the fractionalization affect not only the ground state properties but also thermodynamic behavior in a peculiar manner. We here investigate how the spin dynamics evolves from the high-temperature paramagnet to the quantum spin liquid ground state, for the Kitaev spin model describing the fractionalization into itinerant matter fermions and localized Z2 gauge fluxes. Beyond the previous study [J. Yoshitake, J. Nasu, and Y. Motome, Phys. Rev. Lett. 117, 157203 (2016)], in which the mean-field nature of the cluster dynamical mean-field theory prevented us from studying low-temperature properties, we develop a numerical technique by applying the continuous-time quantum Monte Carlo (CTQMC) method to statistical samples generated by the quantum Monte Carlo (QMC) method in a Majorana fermion representation. This QMC+CTQMC method is fully unbiased and enables us to investigate the low-temperature spin dynamics dominated by thermally excited gauge fluxes, including the unconventional phase transition caused by gauge flux loops in three dimensions, which was unreachable by the previous methods. We apply this technique to the Kitaev model in both two and three dimensions. Our results clearly distinguish two cases: while the dynamics changes smoothly through the crossover in the two-dimensional honeycomb case, it exhibits singular behaviors at the phase transition in the three-dimensional hyperhoneycomb case. We show that the low-temperature spin dynamics is a sensitive probe for thermally fluctuating gauge fluxes that behave very differently between two and three dimensions.

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Incarnation of Majorana Fermions in Kitaev Quantum Spin Lattice

Cited by 10 publications

References 21 publications

Majorana dynamical mean-field study of spin dynamics at finite temperatures in the honeycomb Kitaev model

Majorana dynamical mean-field study of spin dynamics at finite temperatures in the honeycomb Kitaev model

Observation of two types of fractional excitation in the Kitaev honeycomb magnet

Temperature evolution of spin dynamics in two- and three-dimensional Kitaev models: Influence of fluctuating Z2 flux

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