Where Is The Quantum Spin Nematic?

Our work offers the most definitive and unbiased study to date of the phase diagram of the paradigmatic model that has been recently proposed to host the quantum spin-nematic state, an elusive quantum analogue of a liquid crystal. Despite numerous theoretical and experimental efforts, the existence of the spin nematic state remains controversial. In our work, we employed a combination of rigorous analytical and unbiased density-matrix renormalization group approaches, which unambiguously established the extent of the spin nematic phase in a paradigmatic J₁-J₂ ferro-antiferromagnetic model on the square lattice, provided detailed insights into the microscopic nature of this phase, and elucidated general criteria for its stability that should be applicable to all other potential realizations of such phases. Our work also provides vital guidance to the intense experimental searches of the quantum spin nematics, arming them with realistic expectations. Our study advances understanding of the generic guiding principles in the search for the quantum spin nematics, emphasizing the importance of the restrictive many-body effects in the suppression of the analog of the superfluid stiffness in them, which are systematically neglected in the prior theoretical works. We also provide deep connections to the broader physics context, such as the symmetry of the bound states and their Bose-Einstein condensation. Our conclusions and phase diagram should be common to other models.