Probing Spin Liquid Phases in the Kitaev Honeycomb Model using Hierarchical Mean-Field Theory

Hierarchical mean-field theory (HMFT) identifies relevant cluster degrees of freedom while preserving all symmetries of the full model Hamiltonian, thus dealing with competing orders on an equal footing. This approach has been successfully applied to frustrated quantum spin and bosonic systems. A question remains: How reliable is the method when applied to models displaying phases with topological quantum order? Using the HMFT we recover an accurate phase diagram of the exactly-solvable Kitaev Honeycomb model, which is one of the paradigmatic 2D models hosting quantum spin liquid phases. This constitutes an excellent starting point to explore other potential spin-liquid phases occurring when magnetic field and additional interactions are added to the model.