Quantum phases in the honeycomb-lattice J1 – J3 ferro-antiferromagnetic model

Using large-scale density-matrix renormalzation group calculations and minimally augmented spin-wave theory, we demonstrate that the phase diagram of the quantum $S=\frac{1}{2}\phantom{\rule{4pt}{0ex}}{J}_{1}$--${J}_{3}$ ferro-antiferromagnetic model on the honeycomb lattice differs dramatically from the classical one. It hosts the double-zigzag and Ising-$z$ phases as unexpected intermediaries between ferromagnetic and zigzag states that are also extended beyond their classical regions of stability. In broad agreement with quantum order-by-disorder arguments, these collinear phases replace the classical spiral state.