Field-revealed gapless spin liquid and hidden chiral order in a hierarchical mean-field theory study of an extended Kitaev honeycomb model

The Kitaev honeycomb model is an emblematic example of a topologically ordered quantum spin liquid. Due to its exact solvability, the model provides a benchmark for evaluating the success of numerical methods that can be applied to nonintegrable models with similar behaviors. In this work, we apply hierarchical mean-field theory (HMFT) to the Kitaev model and its nonintegrable extensions. HMFT is a cluster mean-field theory that has been shown to accurately capture the thermodynamic limit phase diagrams of frustrated magnetic systems in an unbiased manner using minimal computational resources. In applying it to the Kitaev model, we provide the first example of the technique’s success in modeling a gapless topologically ordered system, as well as unveil a potential hidden chiral order in the model via controlled symmetry breaking. In addition, we apply HMFT to the model in the presence of a strong magnetic field, found in previous work to have a potential U(1) gapless spin liquid phase. The previous results were obtained via exact-diagonalization on small clusters and density-matrix renormalization group on thin strips. Both geometries present difficulties in extrapolating to a full two-dimensional infinite system, while this information is inherently captured by our HMFT study.