Where is the Quantum Spin Nematic? And Beyond.

Quantum spin nematics and unconventional magnetically ordered phases are among the exotic states that can be stabilized in quantum magnets with competing interactions. I will report on our recent results concerning paradigmatic S=1/2 J₁-J₂ square-lattice [1] and J₁-J₃ honeycomb-lattice [2] ferro-antiferromagnetic models, with the former focusing on the search for the quantum spin nematics and the latter on the emergence of the classically unstable quantum phases, potentially relevant to a large group of Kitaev materials. The very recent work on some strong Kitaev material candidates will be reported too. The minimally-augmented spin-wave theory is advertised as an effective tool to explore quantum phases beyond their classically stable ranges. Our works provides vital guidance to the intense experimental searches of the quantum spin nematics and other unconventional quantum phases, arming them with realistic expectations.