Ultracold atoms and molecules trapped in optical lattices are expected to serve as simulators of strongly correlated systems and topological states of matter. A fascinating example is to realize the Kitaev quantum spin liquid by using ultracold polar molecules. However, although experimental implementation of the Kitaev-type interaction was proposed, the stability of the Kitaev quantum spin liquid has not been fully investigated thus far. Here we study a quantum spin model with long-range angle-dependent Kitaev-type interactions proposed for the polar molecules, by the pseudofermion functional renormalization group method. We reveal that the ground state is magnetically ordered in both ferromagnetic and antiferromagnetic models regardless of the spatial anisotropy of the interactions, while the isotropic case is most frustrated and closest to the realization of the Kitaev quantum spin liquid. Furthermore, by introducing a cutoff in the interaction range, we clarify how the Kitaev quantum spin liquid is destroyed by the long-range interactions. The results urge us to reconsider the feasibility of the Kitaev quantum spin liquid in ultracold polar molecules.
The realization of quantum spin liquids (QSLs) in Kitaev magnets represents an intriguing topic in frustrated quantum magnetism. Despite prediction in the pure Kitaev honeycomb model, realization of QSLs in realistic systems and materials remain scarce. The recent discovery of cobalt-based compound Na
2Co
2TeO
6 has raised significant research interest. By establishing a realistic
K-
J-
Γ-
Γ′ model for Na
2Co
2TeO
6 -- with a dominant antiferromagnetic (AFM) Kitaev interaction (
K>0) that quantitatively explains its thermodynamics measurements -- we reveal an intermediate gapless QSL phase under [111] magnetic fields with tensor-network calculations. We confirm the QSL nature of this phase by demonstrating its adiabatic connection to the intensively studied intermediate QSL of the pure AFM Kitaev model under out-of-plane fields. Our results show excellent agreement with recent high-field experiments, thereby explaining the intermediate-field phase in Na
2Co
2TeO
6. These findings bridge the gap between theoretical proposals for a Kitaev-derived QSL and experimental realization, opening new avenues for exploring exotic quantum states of matter in realistic Kitaev materials.
The spin-1/2 Kitaev model offers the exactly solvable example of quantum spin liquids.Possible material realizations of the spin-1/2 Kitaev systems and the prospect of using the Majorana fermion excitations for quantum computations have revolutionized quantum spin liquids research.Recently it has been suggested that higher-spin, especially spin-1, Kitaev exchange interactions can be realized in a variety of materials.Numerical computations on small clusters indicate that the ground state of the spin-1 Kitaev model may also be a quantum spin liquid.On the other hand, the nature of the ground state remains elusive since the spin-1 model is not exactly solvable in contrast to the spin-1/2 model.In this work, using the quantum-entanglement based tensor network approach, we construct an explicit ground-state wave function for the spin-1 Kitaev model, which is written only in terms of physical spin operators.We establish the existence of distinct topological sectors on a torus by constructing the minimally entangled states in the degenerate ground-state manifold and evaluating topological entanglement entropy.Our results suggest that the ground state of the spin-1 Kitaev model is a gapped quantum spin liquid with Z 2 gauge structure and Abelian quasiparticles.We explain the subtle differences between the spin-1/2 and spin-1 Kitaev quantum spin liquids.