Characterizing emergent spin liquids in the extended Kitaev honeycomb model: a hierarchical mean-field approach

The Kitaev honeycomb model represents a paradigmatic example of a topologically-ordered quantum spin liquid (the Kitaev spin liquid, or KSL). Due to its exactly-solvable nature, a great deal is known about the properties of its ground state phases. Recent theoretical work has demonstrated a rich array of states generated by adding additional terms to the Kitaev model, even in the case of a simple applied magnetic field. We study the Kitaev model in external magnetic field with hierarchical mean-field theory (HMFT), a method based on the use of clusters as the basic degrees of freedom that allows to uncover phase diagrams of frustrated quantum magnetism in the thermodynamic limit. Benchmark numerical results with clusters of up to 24 spins and finite size scaling show that HMFT accurately describes the exact phase diagram at zero field, allowing us to identify the gapless Kitaev spin liquid as a chiral magnet whose long range order vanishes upon increasing the cluster size. Upon adding a [111] external magnetic field, we find a phase diagram hosting various phases characterized by chirality and nonzero topological entanglement entropy, in qualitative agreement with other methods, as well as an intermediate partially polarized phase with topological order that has not been previously identified.