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
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
The possible existence of a quantum spin liquid (QSL) phase, an exotic state of matter with long-range quantum entanglement and fractionalized excitations, in
α-RuCl
3 has sparked widespread interests in exploring QSLs in various Kitaev models under magnetic fields. Recently, a
K-
J-
Γ-
Γ′ model has been proposed to accurately describe the compound by fitting the measured thermodynamic data, where
J is Heisenberg interaction, and
Γ,
Γ′ are off-diagonal exchanges on top of the dominant Kitaev coupling
K. Based on this effective model, an intermediate QSL phase in presence of an out-of-plane fields along the
[111] direction, between the low-field zigzag order and high-field polarized phase, has been predicted. By combining density matrix renormalization group (DMRG), exponential tensor renormalization group (XTRG), and variational Monte Carlo (VMC) calculations, we address the nature of this QSL phase in the honeycomb
K-
J-
Γ-
Γ′ model under the
[111]-direction field. Our DMRG calculations find the algebraic-like decay of spin correlation function, the finite spin scalar chiral order, and lattice nematic order. Together with the XTRG results of power-law specific heat at low temperature, our findings naturally suggest a gapless nematic chiral spin liquid. On the other hand, our VMC study finds a gapped nematic chiral spin liquid with the variational energy very close to that obtained in DMRG. As VMC finds a very small gap that is beyond the current resolution of both ground-state DMRG and finite-temperature XTRG calculations on finite-width cylinders, we resort the full clarification for the nature of the intermediate QSL to future studies. Lastly, we discuss the implications of our results to the recent experiment on
α-RuCl
3 and the QSL-like phase in a similar
K-
Γ-
Γ′ model.
While U ( 1 ) spin liquids have been extensively studied in both quantum and classical regimes, exact classical Z 2 spin liquids arising from models with nearest-neighbor, bilinear spin interactions are still rare. In this Letter, we explore the four-color Kitaev model as a minimal model for stabilizing classical Z 2 spin liquids across a broad family of tricoordinated lattices. By formulating a Z 2 lattice gauge theory, we identify this spin liquid as being described by an emergent Gauss's law with effective charge-2 condensation, and deconfined fractionalized bond-charge excitations. We complement our findings with Monte Carlo simulations, revealing a crossover from a high-temperature paramagnet to a low-temperature liquid phase characterized by residual entropy, classical Z 2 flux order, and diffuse spin structure factors.
Frustration in quantum spin systems promote a variety of novel quantum phases. An important example is the frustrated spin-1 model on the square lattice with the nearest-neighbor bilinear (
J1) and biquadratic (
K1) interactions. We provide strong evidence for a nematic spin liquid phase in a range of
K1/J1 near the SU(3)-symmetric point (
J1=K1), based on the linear flavor-wave theory and extensive density matrix renormalization group calculation. This phase displays no spin dipolar or quadrupolar order, preserves translational symmetry but spontaneously breaks
C4 lattice rotational symmetry, and possesses fluctuations peaked at the wave vector $(\ensuremath{\pi},2\ensuremath{\pi}/3)$. The spin excitation gap drops rapidly with system size and appears to be gapless, and the nematic order is attributed to the dominant $(\ensuremath{\pi},2\ensuremath{\pi}/3)$ fluctuations. Our results provide a novel mechanism for electronic nematic order and, more generally, open up a new avenue to explore frustration-induced exotic ground states.
Kitaev magnets have emerged as pivotal systems for investigating frustrated magnetism, providing a unique platform to explore quantum phases governed by the interplay between bond-dependent anisotropy and external magnetic fields. However, the quantum phase diagrams, particularly near the dominant antiferromagnetic Kitaev regime, remain puzzling despite extensive studies. In this work, we perform unbiased exact diagonalization calculations of the Kitaev-
Γ model in a [111] magnetic field on a
C6-symmetric 24-site cluster. By calculating the
Z2 flux density and the topological entanglement entropy, we reveal multiple phase transitions and identify signatures of both scalar and vector chiral orders in the intermediate-field regime between the Kitaev spin liquid and the polarized phase. As the negative
Γ interaction increases, we discover a proximate quantum spin liquid featured by a three-peak specific heat and a spin-flop phase at a moderate magnetic field. Our findings provide insight into the field-induced intermediate phases in the antiferromagnetic Kitaev model and pave the way for the hunt for emergent phases in real materials.
The Kitaev chiral spin liquid has captured widespread interest in recent decades because of its intrinsic non-Abelian excitations, yet the experimental realization is challenging. Here we propose to realize and detect Kitaev chiral spin liquid in a deformed honeycomb array of Rydberg atoms. With a laser-assisted dipole-dipole interaction mechanism which realizes both effective hopping and pairing terms for hard-core bosons, together with van der Waals interactions, we achieve the pure Kitaev model with high precision. The gapped non-Abelian spin liquid phase is then obtained under experimental conditions. Moreover, we propose innovative strategies to probe the chiral Majorana edge modes by light Bragg scattering and by imagining their chiral motion. Our proposed scheme broadens the range of quantum spin models with exotic topological phases that can be realized and detected in atomic systems, and makes an important step toward manipulating non-Abelian anyons. Published by the American Physical Society 2024