Quantum Spin Liquid phases in extended Kitaev models on the Honeycomb Lattice*

Kitaev materials have attracted great attention thanks to their potential for realizing the Kitaev model, an exactly solvable spin model that hosts topological quantum spin liquids. However, most Kitaev materials undergo phase transition into a magnetically ordered phase at low temperatures, indicating that non-Kitaev interactions are non-neglectible. Recent experiments on the Kitaev material α-RuCl₃ showed that, under very low temperature an intermediate in-plane magnetic field can suppress the static zigzag magnetic order and induce a liquid-like disordered phase. The nature of the field-induced disordered phase was not fully understood. Motivated by this issue, we studied the K-Γ model (K =6.8 meV and Γ= 9.5meV) which was the minimal model prosed to describe the low-energy physics of α-RuCl₃. From variational Monte Carlo calculations, we found that in-plane magnetic field can indeed cause a phase transition from a zigzag ordered phase into a gapless U(1) Dirac spin liquid phase [1]. Our results semi-quatitatively explain the observed temperature dependence of spin-lattice relaxation rate 1/T₁~T³ in a recent nuclear magnetic resonance experiment [2]. It was also shown that an out-of-plane magnetic field can induce a Kalmeyer-Laughlin-type abelian chiral spin liquid phase, which would show an integer-quantized thermal Hall effect. Our theory hopefully captures the low energy physics of α-RuCl₃ and provides a clue to undertand the experiments in related materials.

[1] Zheng-Xin Liu and B. Normand, Phys. Rev. Lett. 120, 187201 (2018).
[2] J. Zheng, K. Ran, T. Li, J.Wang, P.Wang, B. Liu, Z.-X. Liu, B. Normand, J. Wen, and W. Yu, Phys. Rev. Lett. 119, 227208
(2017).