Quantum stabilization of unexpected ordered phases on the honeycomb lattice

We demonstrate the versatility, simplicity, and power of the minimally augmented spin-wave theory in studying phase diagrams of the quantum spin models in which unexpected magnetically ordered phases occur or the existing ones expand beyond their classical stability regions. We use this method to obtain approximate phase diagrams of the two paradigmatic spin-$\frac{1}{2}$ models on the honeycomb lattice: the ${J}_{1}\text{\ensuremath{-}}{J}_{3}$ ferro-antiferromagnetic and ${J}_{1}\text{\ensuremath{-}}{J}_{2}$ antiferromagnetic $XXZ$ models. For the ${J}_{1}\text{\ensuremath{-}}{J}_{3}$ case, various combinations of the $XXZ$ anisotropies are analyzed. In a dramatic deviation from their classical phase diagrams, which host significant regions of the noncollinear spiral phases, quantum fluctuations stabilize several unconventional collinear phases and significantly extend conventional ones to completely supersede spiral states. These results are in close agreement with the available density-matrix renormalization group calculations. The applicability of this approach to the other models and its potential extension to different types of orders are discussed.