Spin nematic correlations in bilinear-biquadratic S=1 spin chains

TL;DR

This paper investigates spin quadrupolar correlations in bilinear-biquadratic S=1 chains using numerical methods, clarifying the nature of correlations in the gapless phase, exploring the existence of a ferroquadrupolar phase, and analyzing the effects of coupling chains.

Contribution

It provides a detailed numerical analysis of quadrupolar correlations, clarifies the dominant correlations in the gapless phase, and studies the evolution of phases in coupled chain systems.

Findings

Quadrupolar correlations dominate in the gapless phase for theta in (pi/4, pi/2).

The dimerized phase disappears rapidly when chains are coupled, replaced by a gapped phase.

The gapped phase is connected to the Haldane phase and the plaquette phase of the ladder.

Abstract

We present an extensive numerical study of spin quadrupolar correlations in single and coupled bilinear-biquadratic spin one chains, using several methods such as Exact Diagonalization, Density Matrix Renormalization Group and strong coupling series expansions. For the single chain we clarify the dominant correlation function in the enigmatic gapless period-three phase for theta in (pi/4,pi/2), which is of spin quadrupolar nature with a period three spatial structure. Then we revisit the open problem of the possible existence of a ferroquadrupolar phase between the dimerized and the ferromagnetic phases. Although an extended critical region is in principle compatible with the numerical results, a scenario with a huge crossover scale is more plausible. Finally we study the fate of the dimerized phase upon coupling two chains in a ladder geometry. The dimerized phase rapidly vanishes and an extended gapped phase takes over. This gapped phase presumably has dominant short-ranged ferroquadrupolar correlations for theta in (-3pi,4,-pi/2) and -- suprisingly -- seems to be adiabatically connected to the plaquette single solid phase of the Heisenberg S=1 ladder and therefore also with the Haldane phase of isolated chains.