Where is the Quantum Spin Nematic?

TL;DR

This paper provides evidence for the existence of a spin-nematic phase in a specific magnetic model, revealing how interactions and many-body effects influence its stability and phase diagram.

Contribution

It combines analytical and numerical methods to identify and characterize the spin-nematic phase in the $J_1$--$J_2$ model, including the effects of pair interactions and many-body phenomena.

Findings

Nematic phase exists near the pair-condensation field.

First-order transition prevents nematic state at zero field.

Many-body effects significantly reduce the nematic phase region.

Abstract

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 na\"ive expectations. The proposed phase diagram should be broadly valid.