Where is the Quantum Spin Nematic?

We provide strong evidence of the spin-nematic state in a paradigmatic ferro-antiferromagnetic $J_1$–$J_2$ model using analytical and density-matrix renormalization group methods. In zero field, the attraction of spin-flip pairs leads to a first-order transition and no nematic state, while pair-repulsion at larger $J_2$ stabilizes the nematic phase in a narrow region near the pair-condensation field. A devil’s staircase of multi-pair condensates is conjectured for weak pair-attraction. A suppression of the spin-flip gap by many-body effects leads to an order-of-magnitude contraction of the nematic phase compared to naïve expectations. The proposed phase diagram should be broadly valid.