Motivated by recent experiments on $\ensuremath{\alpha}\ensuremath{-}{\mathrm{RuCl}}_{3}$, we investigate a possible quantum spin liquid ground state of the honeycomb-lattice spin model with bond-dependent interactions. We consider the $K\ensuremath{-}\mathrm{\ensuremath{\Gamma}}$ model, where
K and $\mathrm{\ensuremath{\Gamma}}$ represent the Kitaev and symmetric-anisotropic interactions between spin-1/2 moments on the honeycomb lattice. Using the infinite density matrix renormalization group, we provide compelling evidence for the existence of quantum spin liquid phases in an extended region of the phase diagram. In particular, we use transfer-matrix spectra to show the evolution of two-particle excitations with well-defined two-dimensional dispersion, which is a strong signature of a quantum spin liquid. These results are compared with predictions from Majorana mean-field theory and used to infer the quasiparticle excitation spectra. Further, we compute the dynamical structure factor using finite-size cluster computations and show that the results resemble the scattering continuum seen in neutron-scattering experiments on $\ensuremath{\alpha}\ensuremath{-}{\mathrm{RuCl}}_{3}$. We discuss these results in light of recent and future experiments.
In the field of quantum magnetism, the exactly solvable Kitaev honeycomb model serves as a paradigm for the fractionalization of spin degrees of freedom and the formation of [Formula: see text] quantum spin liquids. An intense experimental search has led to the discovery of a number of spin-orbit entangled Mott insulators that realize its characteristic bond-directional interactions and, in the presence of magnetic fields, exhibit no indications of long-range order. Here, we map out the complete phase diagram of the Kitaev model in tilted magnetic fields and report the emergence of a distinct gapless quantum spin liquid at intermediate field strengths. Analyzing a number of static, dynamical, and finite temperature quantities using numerical exact diagonalization techniques, we find strong evidence that this phase exhibits gapless fermions coupled to a massless U(1) gauge field. We discuss its stability in the presence of perturbations that naturally arise in spin-orbit entangled candidate materials.
We develop a gauge-invariant renormalized mean-field theory (RMFT) to reliably find the quantum spin liquid (QSL) states and their field response for realistic Kitaev materials under strong magnetic fields and described by the generalized Kitaev J-K-Γ-
Γ′ model. Remarkably, while our RMFT reproduces previous results based on using more complicated numerical methods, it also predicts several new stable QSL states. In particular, since Kitaev spin liquid (KSL) is no longer a saddle point solution, a new exotic 2-cone state distinct from the KSL is found to describe experimental observations well, and hence should be the candidate state realized in the Kitaev material, α-RuCl3. We further explore the mechanism for the suppression of the observed thermal Hall conductivity at low temperatures within the fermionic framework, and show that the polar-angle dependence of the fermionic gap can distinguish the found 2-cone state from the KSL state in further experiments.
Abstract Large anisotropic exchange in 5 d and 4 d oxides and halides open the door to new types of magnetic ground states and excitations, inconceivable a decade ago. A prominent case is the Kitaev spin liquid, host of remarkable properties such as protection of quantum information and the emergence of Majorana fermions. Here we discuss the promise for spin-liquid behavior in the 4 d 5 honeycomb halide α -RuCl 3 . From advanced electronic-structure calculations, we find that the Kitaev interaction is ferromagnetic, as in 5 d 5 iridium honeycomb oxides, and indeed defines the largest superexchange energy scale. A ferromagnetic Kitaev coupling is also supported by a detailed analysis of the field-dependent magnetization. Using exact diagonalization and density-matrix renormalization group techniques for extended Kitaev-Heisenberg spin Hamiltonians, we find indications for a transition from zigzag order to a gapped spin liquid when applying magnetic field. Our results offer a unified picture on recent magnetic and spectroscopic measurements on this material and open new perspectives on the prospect of realizing quantum spin liquids in d 5 halides and oxides in general.
The quantum spin liquid (QSL) state of Kitaev-like materials, such as iridium oxides A 2IrO3 and α-RuCl3, has been explored in depth. The half-filled Kitaev–Hubbard model with bond-dependent hopping terms is used to describe the Kitaev-like materials, which is calculated using the state-of-the-art fermionic projected entangled pair states method. We find a QSL phase near the Mott insulator transition, which has a strong first-order transition to the semi-metal phase with the decrease of Hubbard U. We suggest that a promising approach to finding QSL states is by finding iridium oxides that are near the Mott insulator transition.
In the search for quantum spin liquids, candidate materials for the Kitaev model and its extensions have been intensively explored during the past decade, as the models realize the exact quantum spin liquids in the ground state. Thus far, insulating magnets in the low-spin
d5 electron configuration under the strong spin-orbit coupling have been studied for realizing the Kitaev-type bond-dependent anisotropic interactions between the spin-orbital entangled Kramers doublets. To extend the candidates, here we investigate the systems in a high-spin
d7 electron configuration, whose ground state is described by the spin-orbital entangled Kramers doublet. By the second-order perturbation in terms of the ${t}_{2g}\ensuremath{-}{t}_{2g}$ and ${t}_{2g}\ensuremath{-}{e}_{g}$ hoppings, we show that the effective spin model possesses the anisotropic Kitaev interactions as well as the isotropic Heisenberg ones. While the Kitaev interaction is always ferromagnetic, the Heisenberg interaction can become either ferromagnetic or antiferromagnetic depending on the Coulomb interactions and the crystalline electric fields. We also derive the effective model for the low-spin
d5 electron configuration within the same perturbation scheme, in which the Kitaev interaction becomes both ferromagnetic and antiferromagnetic, while the Heisenberg one is always ferromagnetic. Referring to the previous study for the Kitaev-Heisenberg model, we find that the quantum spin liquid phase exists in the reasonable parameter region in both
d7 and
d5 cases, while the former has a richer structure of the phase diagram. We discuss the advantages of the
d7 case in comparison with the
d5 case. Our results indicate that the high-spin
d7 state provides another platform for the Kitaev-type quantum spin liquid.