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The Kitaev model provides us with a rare example of exact quantum spin liquid (QSL) states in more than one dimension. While it is very important to explore new platforms for realizing the Kitaev QSL theoretically, extensions of the model make it no longer solvable and numerical calculations are challenging. Here we address the feasibility of the Kitaev QSL for three extensions of the model, by using the pseudofermion functional renormalization group method.

The first one is the extension to higher-spin systems [1]. We clarify the ground-state phase diagrams of the spin-S Kitaev-Heisenberg model systematically by changing the ratio between the Kitaev and Heisenberg interactions and the length of spin S. We find that the Kitaev QSL regions remain stable for S < 2, whereas the regions are quickly shrunk while increasing S.

The second one is the extension to three-dimensional (3D) systems [2]. Studying the Kitaev-Heisenberg model defined on a 3D hyperhoneycomb lattice, we show that the ground-state phase diagram is 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.

The last one is for ultracold polar molecules trapped in an optical lattice [3]. We study a model proposed as an implementation of the Kitaev-type interactions, and clarify that the ground state is magnetically ordered. We also unravel how the Kitaev QSL is destabilized by the long-range interactions originating from the dipole interactions between polar molecules.

[1] K. Fukui, Y. Kato, J. Nasu, and Y. Motome, Phys. Rev. B 106, 174416 (2022).

[2] K. Fukui, Y. Kato, and Y. Motome, J. Phys. Soc. Jpn. 92, 064708 (2023).

[3] K. Fukui, Y. Kato, J. Nasu, and Y. Motome, Phys. Rev. B 106, 014419 (2022).

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