Emergent magnetic order in the antiferromagnetic Kitaev model in a 111 field

The Kitaev spin liquid, stabilized as the ground state of the Kitaev honeycomb model, is a paradigmatic example of a topological Z₂ quantum spin liquid. The fate of the Kitaev spin liquid in presence of an external magnetic field is at present, a subject of intense scrutiny due to recent experimental signatures pointing to a Z₂ topological phase in certain materials, as well as theoretical studies predicting the emergence of a quantum spin liquid phase of debated nature. In this work, we employ hierarchical mean-field theory, a method based on the use of clusters preserving relevant symmetries and short-range quantum correlations, to investigate the quantum phase diagram of the antiferromagnetic Kitaev's model in a 111 magnetic field. By using clusters of 24 sites, we predict that the Kitaev spin liquid transits through two intermediate phases, characterized by emerging stripe and chiral orders, respectively, before entering the trivial partially polarized phase, differing from previous studies. We assess our results by performing exact diagonalization and computing the scaling of different observables, including the many-body Chern number and other topological quantities, thus establishing hierarchical mean-field theory as a method to study models of frustrated quantum magnetism potentially hosting topological quantum spin liquids.