Quantum phase transitions of extended Kitaev Model

The Kitaev model is a rare example which is an exactly solvable model of a spin liquid state and also has many candidate materials that contain the required bond-dependent Ising-like interaction. Although most of candidate materials become magnetic ordered at the lowest temperature under experimental conditions, anomalous observations supporting the Kitaev spin liquid are reported when an external magnetic field is applied. Therefore, these Kitaev materials are speculated to be in proximity to the spin liquid phase and can be driven to this liquid phase under external field. In this talk, I will discuss the phase transitions between these distinct states induced by various types of interactions or magnetic fields through a variational scheme. This approach becomes exact in the pure Kitaev limit and is highly relevant to materials with dominant Kitaev interactions. Under different types of perturbations, it successfully describes the quantum phase transitions from the (pure) Kitaev spin liquid to various magnetic orderings via the condensation of preformed bound states of fractional particles or several distinct Abelian spin liquids via a topological phase transition. Given the good agreement with the existing numerical studies, this variational approach provides us with valuable insights about the Kitaev materials.