The Kitaev-Heisenberg model defined on both honeycomb and triangular lattices has been studied intensively in recent years as a possible model to describe spin-orbital physics in iridium oxides. In the model, there are many phases characteristic for each lattice. However, there is no study of how the phases in the two lattices merge with each other when geometry changes from the honeycomb lattice to triangular lattice. We investigate the ground state of the Kitaev-Heisenberg model defined on the system connecting the honeycomb and triangular lattices, named a honeycomb-triangular lattice. We obtain a ground state phase diagram of this model with classical spins by using the Luttinger-Tisza method and classical Monte Carlo simulation. In addition to known phases in the honeycomb and triangular lattices, we find coexisting phases consisting of the known phases. From the exact diagonalization and density-matrix renormalization-group calculations for the model with quantum spins, we find phases similar to the classical results, implying a small effect of quantum fluctuation on the phase diagram.
We study the Kitaev--Heisenberg model on a triangular lattice by using the two-dimensional density-matrix renormalization group method. Calculating the ground-state energy and spin structure factors, we obtain a ground-state phase diagram of the Kitaev--Heisenberg model. As suggested by previous studies, we find a 120
∘ antiferromagnetic (AFM) phase, a
Z2-vortex crystal phase, a nematic phase, a dual
Z2-vortex crystal phase (the dual counterpart of the
Z2-vortex crystal phase), a
Z6 ferromagnetic phase, and a dual ferromagnetic phase (the dual counterpart of the $\mathbb{Z}_6 $ ferromagnetic phase). Spin correlations discontinuously change at phase boundaries because of first-order phase transitions. We also study the relation among the von Neumann entanglement entropy, entanglement spectrum, and phase transitions of the model. We find that the Schmidt gap closes at phase boundaries and thus the entanglement entropy clearly changes as well. This is different from the Kitaev--Heisenberg model on a honeycomb lattice, where the Schmidt gap and entanglement entropy are not necessarily a good measure of phase transitions.
Abstract We study the ground state of the 1D Kitaev-Heisenberg (KH) model using the density-matrix renormalization group and Lanczos exact diagonalization methods. We obtain a rich ground-state phase diagram as a function of the ratio between Heisenberg (J = cosϕ) and Kitaev (K = sinϕ) interactions. Depending on the ratio, the system exhibits four long-range ordered states: ferromagnetic-z, ferromagnetic-xy, staggered-xy, Néel-z, and two liquid states: Tomonaga-Luttinger liquid and spiral-xy. The two Kitaev points
ϕ=2π ϕ=π2 and
φ=23π φ=3π2 are singular. Theϕ-dependent phase diagram is similar to that for the 2D honeycomb-lattice KH model. Remarkably, all the ordered states of the honeycomb-lattice KH model can be interpreted in terms of the coupled KH chains. We also discuss the magnetic structure of the K-intercalated RuCl3, a potential Kitaev material, in the framework of the 1D KH model. Furthermore, we demonstrate that the low-lying excitations of the 1D KH Hamiltonian can be explained within the combination of the known six-vertex model and spin-wave theory.
We study the ground state of the 1D Kitaev-Heisenberg (KH) model using the density-matrix renormalization group and Lanczos exact diagonalization methods. We obtain a rich ground-state phase diagram as a function of the ratio between Heisenberg (J = cosϕ) and Kitaev (K = sinϕ) interactions. Depending on the ratio, the system exhibits four long-range ordered states: ferromagnetic-z, ferromagnetic-xy, staggered-xy, Néel-z, and two liquid states: Tomonaga-Luttinger liquid and spiral-xy. The two Kitaev points ϕ=π2 and φ=3π2 are singular. The ϕ-dependent phase diagram is similar to that for the 2D honeycomb-lattice KH model. Remarkably, all the ordered states of the honeycomb-lattice KH model can be interpreted in terms of the coupled KH chains. We also discuss the magnetic structure of the K-intercalated RuCl3, a potential Kitaev material, in the framework of the 1D KH model. Furthermore, we demonstrate that the low-lying excitations of the 1D KH Hamiltonian can be explained within the combination of the known six-vertex model and spin-wave theory.
The Kitaev model, which hosts a quantum spin liquid (QSL) in the ground state, was originally defined on a two-dimensional honeycomb lattice, but can be straightforwardly extended to any tricoordinate lattices in any spatial dimensions. In particular, the three-dimensional (3D) extensions are of interest as a realization of 3D QSLs, and some materials like
β-Li
2IrO
3,
γ-Li
2IrO
3, and
β-ZnIrO
3 were proposed for the candidates. However, the phase diagrams of the models for those candidates have not been fully elucidated, mainly due to the limitation of numerical methods for 3D frustrated quantum spin systems. Here we study the Kitaev-Heisenberg model defined on a 3D hyperhoneycomb lattice, by using the pseudofermion functional renormalization group method. We show that the ground-state phase diagram contains the QSL phases in the vicinities of the pristine ferromagnetic and antiferromagnetic Kitaev models, in addition to four magnetically ordered phases, similar to the two-dimensional honeycomb case. Our results respect the four-sublattice symmetry inherent in the model, which was violated in the previous study. Moreover, we also show how the phase diagram changes with the anisotropy in the interactions. The results provide a reference for the search of the hyperhoneycomb Kitaev materials.
The celebrated Kitaev honeycomb model provides an analytically tractable example with an exact quantum spin liquid ground state. While in real materials, other types of interactions besides the Kitaev coupling (
K) are present, such as Heisenberg (
J) and symmetric off-diagonal ($\mathrm{\ensuremath{\Gamma}}$) terms, these interactions can also be generalized to a triangular lattice. Here, we carry out a comprehensive study of the $J\ensuremath{-}K\ensuremath{-}\mathrm{\ensuremath{\Gamma}}$ model on a triangular lattice covering the whole parameter region, using a combination of exact diagonalization, classical Monte Carlo, and analytic methods, with an emphasis on the effects of the $\mathrm{\ensuremath{\Gamma}}$ term. In the HK limit ($\mathrm{\ensuremath{\Gamma}}=0$), we find five quantum phases which are quite similar to their classical counterparts. Among them, stripe-A and dual N\'eel phases are robust against the introduction of the $\mathrm{\ensuremath{\Gamma}}$ term, in particular, stripe A extends to the region connecting $K=\ensuremath{-}1$ and
K=1 for $\mathrm{\ensuremath{\Gamma}}<0$. Though the ${120}^{\ensuremath{\circ}}$ N\'eel phase also extends to a finite $\mathrm{\ensuremath{\Gamma}}$, its region is largely reduced compared to the previous classical result. Interestingly, the ferromagnetic (dubbed FM-A) and stripe-B phases are unstable in response to an infinitesimal $\mathrm{\ensuremath{\Gamma}}$ interaction. Moreover, we find five additional phases for $\mathrm{\ensuremath{\Gamma}}\ensuremath{\ne}0$ which are elaborated by both the quantum and classical numerical methods. Part of the parameter space previously identified as the ${120}^{\ensuremath{\circ}}$ N\'eel phase in the classical study is found to give way to the modulated stripe phase. Depending on the sign of the $\mathrm{\ensuremath{\Gamma}}$ term, the FM-A phase transits into FM-B ($\mathrm{\ensuremath{\Gamma}}>0$) and FM-C ($\mathrm{\ensuremath{\Gamma}}<0$) phases with different spin orientations. Similarly, the stripe-B phase transits into stripe-C ($\mathrm{\ensuremath{\Gamma}}>0$) and stripe-A ($\mathrm{\ensuremath{\Gamma}}<0$) phases. Around the positive $\mathrm{\ensuremath{\Gamma}}$ point, due to the interplay of the Heisenberg, Kitaev, and $\mathrm{\ensuremath{\Gamma}}$ interactions, we find a possible quantum spin liquid in a noticeable region with a continuum in spin excitations.
We derive and study a spin one-half Hamiltonian on a honeycomb lattice describing the exchange interactions between Ir4+ ions in a family of layered iridates A2IrO3 (A=Li,Na). Depending on the microscopic parameters, the Hamiltonian interpolates between the Heisenberg and exactly solvable Kitaev models. Exact diagonalization and a complementary spin-wave analysis reveal the presence of an extended spin-liquid phase near the Kitaev limit and a conventional Néel state close to the Heisenberg limit. The two phases are separated by an unusual stripy antiferromagnetic state, which is the exact ground state of the model at the midpoint between two limits.