Probable absence of a quadrupolar spin-nematic phase in the bilinear-biquadratic spin-1 chain

TL;DR

This study uses advanced numerical methods to investigate the phase diagram of a spin-1 chain, providing evidence against the existence of a proposed quadrupolar spin-nematic phase near the ferromagnetic point.

Contribution

It offers a highly accurate numerical analysis that challenges previous suggestions of a nondimerized quantum nematic phase in the bilinear-biquadratic spin-1 chain.

Findings

Order parameter vanishes only at ferromagnetic transition

Nondimerized phase likely absent near the ferromagnetic point

Results do not support the existence of a quadrupolar spin-nematic phase

Abstract

We study numerically the ground-state phase diagram of the bilinear-biquadratic spin-1 chain near the ferromagnetic instability point, where the existence of a gapped or gapless nondimerized quantum nematic phase has been suggested. Our results, obtained by a highly accurate density-matrix renormalization-group (DMRG) calculation are consistent with the view that the order parameter characterizing the dimer phase vanishes only at the point where the system becomes ferromagnetic, although the existence of a gapped or gapless nondimerized phase in a very narrow parameter range between the ferromagnetic and the dimerized regimes cannot be ruled out.