We compute the low-energy excitation spectrum and the dynamical spin structure factor of the Kitaev-Heisenberg-Gamma model through a variational approach based on the exact fractionalized excitations of the pure Kitaev honeycomb model. This novel approach reveals the physical reason for the asymmetric stability of the Kitaev spin liquid phases around the ferromagnetic and antiferromagnetic Kitaev limits. Moreover, we demonstrate that the fractionalized excitations form bound states in specific regions of each Kitaev spin liquid phase and that certain phase transitions induced by Heisenberg and Gamma interactions are driven by the condensation of such a bound state. Remarkably, this bound state appears as a sharp mode in the dynamical spin structure factor, while its condensation patterns at the appropriate phase transitions provide a simple explanation for the magnetically ordered phases surrounding each Kitaev spin liquid phase.
We compute the low-energy excitation spectrum and the dynamical spin structure factor of the Kitaev-Heisenberg-Gamma model through a variational approach based on the exact fractionalized excitations of the pure Kitaev honeycomb model. This novel approach reveals the physical reason for the asymmetric stability of the Kitaev spin liquid phases around the ferromagnetic and antiferromagnetic Kitaev limits. Moreover, we demonstrate that the fractionalized excitations form bound states in specific regions of each Kitaev spin liquid phase and that certain phase transitions induced by Heisenberg and Gamma interactions are driven by the condensation of such a bound state. Remarkably, this bound state appears as a sharp mode in the dynamical spin structure factor, while its condensation patterns at the appropriate phase transitions provide a simple explanation for the magnetically ordered phases surrounding each Kitaev spin liquid phase.
We investigate the generic features of the low energy dynamical spin structure factor of the Kitaev honeycomb quantum spin liquid perturbed away from its exact soluble limit by generic symmetry-allowed exchange couplings. We find that the spin gap persists in the Kitaev-Heisenberg model, but generally vanishes provided more generic symmetry-allowed interactions exist. We formulate the generic expansion of the spin operator in terms of fractionalized Majorana fermion operators according to the symmetry enriched topological order of the Kitaev spin liquid, described by its projective symmetry group. The dynamical spin structure factor displays power-law scaling bounded by Dirac cones in the vicinity of the Γ, K, and K^{'} points of the Brillouin zone, rather than the spin gap found for the exactly soluble point.
We explore the phase diagram of the Kitaev-Heisenberg model with nearest neighbor interactions on the honeycomb lattice using the exact diagonalization of finite systems combined with the cluster mean field approximation, and supplemented by the insights from analytic approaches: the linear spin-wave and second-order perturbation theories. This study confirms that by varying the balance between the Heisenberg and Kitaev term, frustrated exchange interactions stabilize in this model either one of four phases with magnetic long range order: N\'eel phase, ferromagnetic phase, and two other phases with coexisting antiferromagnetic and ferromagnetic bonds, zigzag and stripy phase, or one of two distinct spin-liquid phases. Out of these latter disordered phases, the one with ferromagnetic Kitaev interactions has a substantially broader range of stability as the neighboring competing ordered phases, ferromagnetic and stripy, have very weak quantum fluctuations. Focusing on the quantum spin-liquid phases, we study spatial spin correlations and dynamic spin structure factor of the model by the exact diagonalization technique, and discuss the evolution of gapped low-energy spin response across the quantum phase transitions between the disordered spin liquid and phases with long range magnetic order.
We study the dynamics of fractionalized excitations in a Kitaev spin liquid (KSL) induced by a local magnetic field perpendicular to the Kitaev honeycomb lattice. The local magnetic field induces a dynamic excitation of a pair of fluxes described by a generally particle-hole asymmetric interacting resonant level model and the dynamics resembles that of a Kondo problem. The p-h asymmetry competes with the magnetic field and results in a rich phase diagram. Moreover, the magnetic field breaks the gauge equivalence of the ferromagnetic (FM) and anti-ferromagnetic (AFM) Kitaev couplings of the ground state and leads to dramatically different behaviors for the two cases. The latter experiences a first order phase transition during magnetization whereas the former does not. By studying the response of the KSL to the magnetic field in different regimes, we obtain the RG flow and phase diagram of the system in the whole space. This study can be generalized to the KSL in a uniform magnetic field and help resolve issues in recent experiments on KSL candidates.
The main question we address is how to probe the fractionalized excitations of a quantum spin liquid (QSL), for example, in the Kitaev honeycomb model. By analyzing the energy spectrum and entanglement entropy, for antiferromagnetic couplings and a field along either [111] or [001], we find a gapless QSL phase sandwiched between the non-Abelian Kitaev QSL and polarized phases. Increasing the field strength towards the polarized limit destroys this intermediate QSL phase, resulting in a considerable reduction in the number of frequency modes and the emergence of a beating pattern in the local dynamical correlations, possibly observable in pump-probe experiments.
Schwinger boson perturbation theory for spin-S Kitaev-Heisenberg magnets: phase diagram and dynamical response near Kitaev spin liquids
We develop a Schwinger boson perturbative framework for the spin-S Kitaev-Heisenberg model. The spin-liquid saddle point of the pure Kitaev model is used as the unperturbed state, and magnetic instabilities and dynamical spin correlations are evaluated around this saddle point. We decompose the Hamiltonian exactly into two parts by exploiting the Klein duality intrinsic to the Kitaev-Heisenberg model. We perform the random-phase approximation by taking the part invariant under the duality transformation as the unperturbed term and treating the remaining term, which changes sign under it, as the perturbation. We determine the phase boundaries separating the quantum spin-liquid regimes from the adjacent magnetically ordered phases for S=1/2, 1, 3/2, and 2. The spin-liquid regions shrink rapidly with increasing S and become very narrow at S=2. We also compute the spin dynamics of the spin-S Kitaev-Heisenberg model, focusing on S=1, and find that the dressed dynamical spin structure factor retains a broad two-spinon continuum at finite energies, while the low-energy spectral weight softens at the ordering wave vectors of the adjacent magnetic phases. Our framework thus enables thermodynamic-limit calculations of spin dynamics near magnetic instabilities.
We present an augmented parton mean-field theory which (i) reproduces the exact ground state, spectrum, and dynamics of the quantum spin-liquid phase of Kitaev's honeycomb model, and (ii) is amenable to the inclusion of integrability breaking terms, allowing a perturbation theory from a controlled starting point. Thus, we exemplarily study dynamical spin correlations of the honeycomb Kitaev quantum spin liquid within the $K\ensuremath{-}J\ensuremath{-}\mathrm{\ensuremath{\Gamma}}$ model, which includes Heisenberg and symmetric-anisotropic (pseudodipolar) interactions. This allows us to trace changes of the correlations in the regime of slowly moving fluxes, where the theory captures the dominant deviations when integrability is lost. These include an asymmetric shift together with a broadening of the dominant peak in the response as a function of frequency, the generation of further-neighbor correlations and their structure in real and spin space, and a resulting loss of an approximate rotational symmetry of the structure factor in reciprocal space. We discuss the limitations of this approach and also view the neutron-scattering experiments on the putative proximate quantum spin-liquid material $\ensuremath{\alpha}\text{\ensuremath{-}}{\mathrm{RuCl}}_{3}$ in the light of the results from this extended parton theory.