We study magnetic excitations and thermal Hall effect on the Kitaev-Heisenberg model under magnetic fields. By employing the spin-wave theory for the magnetic orders realized in this model, we examine the topological nature of the spin-wave dispersio
ns and calculate the thermal Hall conductivity. The comprehensive investigations on the field-angle dependence clarify that the thermal Hall conductivity is sensitive to the spin ordered pattern and excitation spectra of magnons; this quantity is enhanced by the noncoplanar spin configurations and small magnon gap in the excitation spectrum. On the other hand, we also find a common feature in the field-angle dependence of the thermal Hall conductivity. It vanishes when the magnetic field is on the planes spanned by the spin axes. We reveal that the behavior is intrinsic to the Kitaev -Heisenberg model in an applied field and demonstrate that the introduction of the off-diagonal spin interaction causes the disappearance of the feature in the thermal Hall conductivity.
We investigate the impact of two types of disorder, bond randomness and site dilution, on the spin dynamics in the Kitaev model on a honeycomb lattice. The ground state of this model is a canonical quantum spin liquid with spin fractionalization into
two types of quasiparticles, itinerant Majorana fermions and localized fluxes. Using unbiased quantum Monte Carlo simulations, we calculate the temperature evolution of the dynamical spin structure factor, the magnetic susceptibility, and the NMR relaxation rate. In the dynamical spin structure factor, we find that the two types of disorder affect seriously the low-energy peak dominantly originating from the flux excitations, rather than the high-energy continuum from the Majorana excitations, in a different way: The bond randomness softens the peak to the lower energy with broadening, whereas the site dilution smears the peak and in addition develops the other sharp peaks inside the spin gap including the zero energy. We show that the zero-energy spin excitations, which originate from the Majorana zero modes induced around the site vacancies, survive up to the temperature comparable to the energy scale of the Kitaev interaction. For the bond randomness, the low-temperature susceptibility does not show any qualitative change against the weak disorder, but it changes to divergent behavior while increasing the strength of disorder. Similar distinct behaviors for the weak and strong disorder are observed also in the NMR relaxation rate; an exponential decay changes into a power-law decay. In contrast, for the site dilution, we find no such crossover; divergent behavior in the susceptibility and a power-law decay in the NMR relaxation rate appear immediately with the introduction of the site dilution. We discuss the relevance of our results to experiments for the Kitaev candidate materials with disorders.
We propose a mechanism of the spin Seebeck effect attributed to excitonic condensation in a nonmagnetic insulator. We analyze a half-filled two-orbital Hubbard model with a crystalline field splitting in the strong coupling limit. In this model, the
competition between the crystalline field and electron correlations brings about an excitonic insulating state, where the two orbitals are spontaneously hybridized. Using the generalized spin-wave theory and Boltzmann transport equation, we find that a spin current generated by a thermal gradient is observed in the excitonic insulating state without magnetic fields. The spin Seebeck effect originates from spin-split collective excitation modes although the ground state does not exhibit any magnetic orderings. This peculiar phenomenon is inherent in the excitonic insulating state, whose order parameter is time-reversal odd and yields a spin splitting for the collective excitation modes. We also find that the spin current is strongly enhanced and its direction is inverted in the vicinity of the phase transition to another magnetically ordered phase. We suggest that the present phenomenon is possibly observed in perovskite cobaltites with the GdFeO$_3$-type lattice distortion.
Effects of the spin-orbit coupling (SOC) and magnetic field on excitonic insulating (EI) states are investigated. We introduce the two-orbital Hubbard model with the crystalline field splitting, which is a minimal model for discussing the exciton con
densation in strongly correlated electron systems, and analyze its effective Hamiltonian in the strong correlation limit by using the mean-field theory. In the absence of the SOC and magnetic field, the ground state changes from the nonmagnetic band-insulating state to the EI state by increasing the Hund coupling. In an applied magnetic field, the magnetic moment appears in the EI state, which is continuously connected to the forced ferromagnetic state. On the other hand, in the presence of the SOC, they are separated by a phase boundary. We find that the magnetic susceptibility is strongly enhanced in the EI phase near the boundary with a small SOC. This peculiar behavior is attributed to the low-energy fluctuation of the spin nematicity inherent in the high-spin local state stabilized by the Hund coupling. The present study not only reveals the impact of the SOC for the EI state but also sheds light on the role of quantum fluctuations of the spin nematicity for the EI state.
Effects of bond randomness and site dilution are systematically investigated for the Kitaev model describing a quantum spin liquid with fractional excitations of itinerant Majorana fermions and localized fluxes. We find that, in the high-temperature
region where the itinerant Majorana fermions release their entropy, both types of disorders suppress the longitudinal thermal conductivity while keeping the specific heat almost unchanged. This suggests that both disorders reduce the mean-free path of the Majorana fermions. On the other hand, in the low-temperature region, the other specific heat peak associated with the entropy release from the localized fluxes is suppressed for both cases, but it is broadened and shifted to the lower-temperature side by the bond randomness, while the position and the width are almost unchanged against the site dilution. Contrasting behavior is also found in the thermal Hall effect under a magnetic field; the half quantization of the thermal Hall conductivity is fragile against the site dilution, while it remains for the bond randomness despite the reduced onset temperature. We discuss the contrasting behavior from the stability of the topological nature by calculating flux condensation and Majorana excitation gap.
We study a ferromagnetic instability in a single-band Hubbard model on the hypercubic lattice away from half filling. Using dynamical mean-field theory with the continuous-time quantum Monte Carlo simulations based on the segment algorithm, we calcul
ate the magnetic susceptibility in the weak and strong coupling regions systematically. We then find how ferromagnetic fluctuations are enhanced when the interaction strength and density of holes are varied. The efficiency of the double flip updates in the Monte Carlo simulations is also addressed.
We investigate ground-state and finite temperature properties of the mixed-spin $(s, S)$ Kitaev model. When one of spins is half-integer and the other is integer, we introduce two kinds of local symmetries, which results in a macroscopic degeneracy i
n each energy level. Applying the exact diagonalization to several clusters with $(s, S)=(1/2, 1)$, we confirm the presence of this large degeneracy in the ground states, in contrast to the conventional Kitaev models. By means of the thermal pure quantum state technique, we calculate the specific heat, entropy, and spin-spin correlations in the system. We find that in the mixed-spin Kitaev model with $(s, S)=(1/2, 1)$, at least, the double peak structure appears in the specific heat and the plateau in the entropy at intermediate temperatures, indicating the existence of the spin fractionalization. Deducing the entropy in the mixed-spin system with $s, Sle 2$ systematically, we clarify that the smaller spin-$s$ is responsible for the thermodynamic properties at higher temperatures.
We study a ferromagnetic instability in a doped single-band Hubbard model by means of dynamical mean-field theory with the continuous-time quantum Monte Carlo simulations. Examining the effect of the strong correlations in the system on the hypercubi
c and Bethe lattice, we find that the ferromagnetically ordered state appears in the former, while it does not in the latter. We also reveal that the ferromagnetic order is more stable in the case that the noninteracting DOS exhibits a slower decay in the high-energy region. The present results suggest that, in the strong-coupling regime, the high-energy part of DOS plays an essential role for the emergence of the ferromagnetically ordered state, in contrast to the Stoner criterion justified in the weak interaction limit.
We study ordered phases with broken translational symmetry in the half-filled three-orbital Hubbard model with antiferromagnetic Hund coupling by means of dynamical mean-field theory (DMFT) and continuous-time quantum Monte Carlo simulations. The sta
bility regions of the antiferro-orbital (AFO), antiferro-magnetic (AFM), and charge density wave (CDW) states are determined by measuring the corresponding order parameters. We introduce two symmetrically distinct AFO order parameters and show that these are the primary order parameters in the phase diagram. The CDW and AFM states appear simultaneously with these two types of AFO orders in the weak and strong coupling region, respectively. The DMFT phase diagram is consistent with the results obtained by the Hartree approximation and strong-coupling perturbation theory. In the weak coupling regime, a nontrivial exponent $beta=3/2$ is found for the CDW order parameter, which is related to the coupling between the CDW and AFO orders in the Landau theory characteristic for the three-orbital model. We also demonstrate the existence of a metallic AFO state without any charge disproportions and magnetic orders, which appears only at finite temperatures.
We investigate the half-filled two-orbital Hubbard model with the crystalline electric field using dynamical mean-field theory combined with the continuous-time quantum Monte Carlo simulations. We systematically study how the interplay of the intra-
and interorbital Coulomb interations together with the Hund coupling realizes the diagonal and off-diagonal ordered states. It is found that the antiferroorbital ordered state is realized in the Hubbard model, in addition to the antiferromagnetically ordered and excitonic states. The competition between the antiferroorbital ordered and excitonic states close to the band insulating state is addressed.
