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The quantum spin liquid is an enigmatic entity that is often hard to characterize within the conventional framework of condensed matter physics. We here present theoretical and numerical evidence for the characterization of a quantum spin liquid phase extending from the exact ground state to a finite critical temperature. We investigate a three-dimensional variant of the Kitaev model on a hyperhoneycomb lattice in the limit of strong anisotropy; the model is mapped onto an effective Ising-type model, where elementary excitations consist of closed loops of flipped Ising-type variables on a diamond lattice. Analyzing this effective model by Monte Carlo simulation, we find a phase transition from the quantum spin liquid to a paramagnet at a finite critical temperature Tc, accompanied by a divergent singularity of the specific heat. We also compute the magnetic properties in terms of the original quantum spins. We find that the magnetic susceptibility exhibits a broad hump above Tc, while it obeys the Curie law at high temperature and approaches a nonzero Van Vleck-type constant at low temperature. Although the susceptibility changes continuously at Tc, its temperature derivative shows a critical divergence at Tc. We also clarify that the dynamical spin correlation function is momentum independent but shows quantized peaks corresponding to discretized excitations. Although the phase transition accompanies no apparent symmetry breaking in terms of the Ising-type variables or of the original quantum spins, we characterize it from a topological viewpoint. We find that, by defining the flux density for loops of the Ising-type variables, the transition can be interpreted as one occurring from the zero-flux quantum spin liquid to the nonzero-flux paramagnet; the latter has a Coulombic nature due to the local constraints. The role of global constraints on the Ising-type variables is examined in comparison with the results in the two-dimensional loop model. The correspondence of our model to the Ising model on a diamond lattice is also discussed. A possible relevance of our results to the recently discovered hyperhoneycomb compound β-Li2IrO3 is mentioned. [ABSTRACT FROM AUTHOR]

The Kitaev quantum spin liquid displays the fractionalization of quantum spins into Majorana fermions. The emergent Majorana edge current is predicted to manifest itself in the form of a finite thermal Hall effect, a feature commonly discussed in topological superconductors. Here we report on thermal Hall conductivity κxy measurements in α-RuCl3, a candidate Kitaev magnet with the two-dimensional honeycomb lattice. In a spin-liquid (Kitaev paramagnetic) state below the temperature characterized by the Kitaev interaction JK/kB~80 K, positive κxy develops gradually upon cooling, demonstrating the presence of highly unusual itinerant excitations. Although the zero-temperature property is masked by the magnetic ordering at TN=7 K, the sign, magnitude, and T dependence of κxy/T at intermediate temperatures follows the predicted trend of the itinerant Majorana excitations. [ABSTRACT FROM AUTHOR]

We study the spin transport through the quantum spin liquid (QSL) by investigating the real-time and real-space dynamics of the Kitaev spin system with zigzag edges using the time-dependent Majorana mean-field theory. After the magnetic-field pulse is introduced to one of the edges, spin moments are excited in the opposite edge region although spin moments are never induced in the Kitaev QSL region. This unusual spin transport originates from the fact that the S=1/2 spins are fractionalized into the itinerant and localized Majorana fermions in the Kitaev system. Although both Majorana fermions are excited by the magnetic pulse, only the itinerant ones flow through the bulk regime without spin excitations, resulting in the spin transport in the Kitaev system despite the presence of a nonzero spin gap. We also demonstrate that this phenomenon can be observed in the system with small Heisenberg interactions using the exact diagonalization.

The Kitaev quantum spin liquid displays the fractionalization of quantum spins into Majorana fermions. The emergent Majorana edge current is predicted to manifest itself in the form of a finite thermal Hall effect, a feature commonly discussed in topological superconductors. Here we report on thermal Hall conductivity κ_{xy} measurements in α-RuCl_{3}, a candidate Kitaev magnet with the two-dimensional honeycomb lattice. In a spin-liquid (Kitaev paramagnetic) state below the temperature characterized by the Kitaev interaction J_{K}/k_{B}∼80  K, positive κ_{xy} develops gradually upon cooling, demonstrating the presence of highly unusual itinerant excitations. Although the zero-temperature property is masked by the magnetic ordering at T_{N}=7  K, the sign, magnitude, and T dependence of κ_{xy}/T at intermediate temperatures follows the predicted trend of the itinerant Majorana excitations.

In conventional insulating magnets, heat is carried by magnons and phonons. In contrast, when the magnets harbor a quantum spin liquid state, emergent quasiparticles from the fractionalization of quantum spins can carry heat. Here, we investigate unconventional thermal transport yielded by such exotic carriers, in both longitudinal and transverse components, for the Kitaev model, whose ground state is exactly shown to be a quantum spin liquid with fractional excitations described as itinerant Majorana fermions and localized Z_{2} fluxes. We find that the longitudinal thermal conductivity exhibits a single peak at a high temperature, while the nonzero frequency component has a peak at a low temperature, reflecting the spin fractionalization. On the other hand, we show that the transverse thermal conductivity is induced by the magnetic field in a wide temperature range up to the energy scale of the bare exchange coupling; while increasing temperature, the transverse response divided by temperature decreases from the quantized value expected for the topologically nontrivial ground state and shows nonmonotonic temperature dependence. These characteristic behaviors provide experimentally accessible evidence of fractional excitations in the proximity to the Kitaev quantum spin liquid.

While phase transitions between magnetic analogs of the three states of matter-a long-range ordered state, paramagnet, and spin liquid-are extensively studied, the possibility of "liquid-liquid" transitions, namely, between different spin liquids, remains elusive. By introducing the additional Ising coupling into the honeycomb Kitaev model with bond asymmetry, we discover that the Kitaev spin liquid turns into a spin-nematic quantum paramagnet before a magnetic order is established by the Ising coupling. The quantum phase transition between the two liquid states accompanies a topological change driven by fractionalized excitations, the Z_{2} gauge fluxes, and is of first order. At finite temperatures, this yields a persisting first-order transition line that terminates at a critical point located deep inside the regime where quantum spins are fractionalized. It is suggested that similar transitions may occur in other perturbed Kitaev magnets with bond asymmetry.

Experimental identification of quantum spin liquids remains a challenge, as the pristine nature is to be seen in asymptotically low temperatures. We here theoretically show that the precursor of quantum spin liquids appears in the spin dynamics in the paramagnetic state over a wide temperature range. Using the cluster dynamical mean-field theory and the continuous-time quantum Monte Carlo method, which are newly developed in the Majorana fermion representation, we calculate the dynamical spin structure factor, relaxation rate in nuclear magnetic resonance, and magnetic susceptibility for the honeycomb Kitaev model whose ground state is a canonical example of the quantum spin liquid. We find that dynamical spin correlations show peculiar temperature and frequency dependence even below the temperature where static correlations saturate. The results provide the experimentally accessible symptoms of the fluctuating fractionalized spins evincing the quantum spin liquids.

Thermodynamic properties of chiral spin liquids are investigated for a variant of the Kitaev model defined on a decorated honeycomb lattice. Using the quantum Monte Carlo simulation, we find that the model exhibits a finite-temperature phase transition associated with the time reversal symmetry breaking, in both topologically trivial and nontrivial regions. Numerical results for the Chern number and the thermal Hall conductivity indicate that the phase transition changes from a continuous to a discontinuous transition as we vary the coupling constants to reach the non-Abelian phase coming from the Abelian phase of the model. In addition, we find as a diagnostic of the chiral spin liquids, successive crossovers with multistage entropy release above the critical temperature, which indicates that the hierarchical fractionalization of a quantum spin occurs differently between the two regions.

The quantum spin liquid is an exotic quantum state of matter in magnets. This state is a spin analog of liquid helium that does not solidify down to the lowest temperature due to strong quantum fluctuations. In conventional fluids, the liquid and gas possess the same symmetry and adiabatically connect to each other by bypassing the critical end point. We find that the situation is qualitatively different in quantum spin liquids realized in a three-dimensional Kitaev model; both gapless and gapped quantum spin liquid phases at low temperatures are always distinguished from the high-temperature paramagnet (spin gas) by a phase transition. The results challenge the common belief that the absence of thermodynamic singularity down to the lowest temperature is a symptom of a quantum spin liquid.

A layered iron oxide RFe2O4 (R denotes rare-earth-metal elements) is an exotic dielectric material with charge-order (CO) driven electric polarization and magnetoelectric effect caused by spin-charge coupling. In this paper, a theory of electronic structure and dielectric property in RFe2O4 is presented. Charge frustration in paired-triangular lattices allows a charge imbalance without inversion symmetry. Spin frustration induces reinforcement of this polar CO by a magnetic ordering. We also analyze an orbital model for the Fe ion which does not show a conventional long-range order.