Besides the exactly solvable spin-1/2 Kitaev model, higher spin- S ones, not exactly solvable, are promising playgrounds for researches on the quantum spin liquid as well. One of the main interests in higher spin- S cases is the interplay between the Kitaev spin liquid (KSL) and spin nematics. We probe this interplay in a spin-1 model on the honeycomb lattice with competing bilinear-biquadratic and Kitaev interactions. Utilizing the 2D infinite projected entangled-pair state (iPEPS), we map out the phase diagram for the ferro-biquadratic interaction. In the phase diagram, we discover the direct phase transitions between the KSL phases and ferro-quadrupolar ordered spin nematic phase, which we call the FQ phase. It has been revealed that the ferro KSL exhibits robustness against perturbations from ferro-quadrupolar interactions. Also, the FQ phase is extended to the parameter region near the antiferro-Kitaev limit. Published by the American Physical Society 2024
Multipolar spin systems provide a rich ground for the emergence of unexpected states of matter due to their enlarged spin degree of freedom. In this study, with a specific emphasis on S = 1 magnets, we explore the interplay between spin nematic states and spin liquids. Based on the foundations laid in the prior work [R. Pohle , ], we investigate the S = 1 Kitaev model with bilinear-biquadratic interactions, which stabilizes, next to Kitaev spin liquid, spin nematic and triple- q phases, also an exotic chiral spin liquid. Through a systematic reduction of the spin degree of freedom—from CP 2 to CP 1 and ultimately to a discrete eight-color model—we provide an intuitive understanding of the nature and origin of this chiral spin liquid. We find that the chiral spin liquid is characterized by an extensive ground-state degeneracy, bound by a residual entropy, extremely short-ranged correlations, a nonzero scalar spin chirality marked by Z 2 flux order, and a gapped continuum of excitations. Our work contributes not only to the specific exploration of S = 1 Kitaev magnets but also to the broader understanding of the importance of multipolar spin degree of freedom on the ground state and excitation properties in quantum magnets. Published by the American Physical Society 2024
We study the spin- S Kitaev-Heisenberg model on the honeycomb lattice for S = 1 / 2 , 1, and 3 / 2 , by using the coupled cluster method (CCM) of microscopic quantum many-body theory. This system is one of the earliest extensions of the Kitaev model and is believed to contain two extended spin liquid phases for any value of the spin quantum number S . We show that the CCM delivers accurate estimates for the phase boundaries of these spin liquid phases, as well as other transition points in the phase diagram. Moreover, we find evidence of two unexpected narrow phases for S = 1 / 2 , one sandwiched between the zigzag and ferromagnetic phases and the other between the Néel and the stripy phases. The results establish the CCM as a versatile numerical technique that can capture the strong quantum-mechanical fluctuations that are inherently present in generalized Kitaev models with competing bond-dependent anisotropies. Published by the American Physical Society 2024
The Kitaev model, whose ground state is a quantum spin liquid (QSL), was originally conceived for spin
S=1/2 moments on a honeycomb lattice. In recent years, the model has been extended to higher
S from both theoretical and experimental interests, but the stability of the QSL ground state has not been systematically clarified for general
S, especially in the presence of other additional interactions, which inevitably exist in candidate materials. Here we study the spin-
S Kitaev-Heisenberg models by using an extension of the pseudofermion functional renormalization group method to general
S. We show that, similar to the
S=1/2 case, the phase diagram for higher
S contains the QSL phases in the vicinities of the pristine ferromagnetic and antiferromagnetic Kitaev models, in addition to four magnetically ordered phases. We find, however, that the QSL phases shrink rapidly with increasing
S, becoming vanishingly narrow for $S\ensuremath{\ge}2$, whereas the phase boundaries between the ordered phases remain almost intact. Our results provide a reference for the search for higher-
S Kitaev materials.
We study the ground-state phase diagram of the spin-
1/2 Kitaev-Heisenberg model on the bilayer honeycomb lattice with large-scale tensor network calculations based on the infinite projected entangled pair state technique as well as high-order series expansions. We find that beyond various magnetically ordered phases, including ferromagnetic, zigzag, antiferromagnetic (AFM) and stripy states, two extended quantum spin liquid phases arise in the proximity of the Kitaev limit. While these ordered phases also appear in the monolayer Kitaev-Heisenberg model, our results further show that a valence bond solid state emerges in a relatively narrow range of parameter space between the AFM and stripy phases, which can be adiabatically connected to isolated Heisenberg dimers. Our results highlight the importance of considering interlayer interactions on the emergence of novel quantum phases in the bilayer Kitaev materials.
We study the quantum-spin-liquid phase in a variant of the Kitaev model where the bonds of the honeycomb lattice are distributed in a Kekul\'e pattern. The system supports gapped and gapless
Z2 quantum spin liquids with interesting differences from the original Kitaev model, the most notable being a gapped
Z2 spin liquid on a kagome lattice. Perturbing the exactly solvable model with antiferromagnetic Heisenberg perturbations, we find a magnetically ordered phase stabilized by a quantum ``order by disorder'' mechanism, as well as an exotic continuous quantum phase transition between the topological spin liquid and this magnetically ordered phase. Using a combination of field theory and Monte Carlo simulations, we find that the transition likely belongs to the $3D\text{\ensuremath{-}}XY\ifmmode\times\else\texttimes\fi{}{Z}_{2}$ universality class.
Motivated by the largely unexplored domain of multipolar ordered spin states in the Kitaev-Heisenberg (KH) systems we investigate the ground state dynamics of the spin-
21 KH model, focusing on quadrupolar (QP) order in two-leg ladder and two-dimensional honeycomb lattice geometries. Employing exact diagonalization and density-matrix renormalization group methods, we analyze the QP order parameter and correlation functions. Our findings reveal a robust QP order across a wide range of the phase diagram, influenced by the interplay between Heisenberg and Kitaev interactions. Notably, we observe an enhancement of QP order near Kitaev quantum spin-liquid (QSL) phases, despite the absence of long-range spin-spin correlations. This highlights a complex relationship between QP order and QSLs, offering different insights into quantum magnetism in low-dimensional systems. Our findings provide a rational explanation for the observed nonlinear magnetic susceptibility in $\ensuremath{\alpha}\text{\ensuremath{-}}{\mathrm{RuCl}}_{3}$.