Absence of a critical nematic phase in the vicinity of the $\rm {SU}(3)$ ferromagnetic point for the one-dimensional spin-1 bilinear-biquadratic model

TL;DR

This study uses tensor network algorithms to show that there is no critical nematic phase near the SU(3) ferromagnetic point in a one-dimensional spin-1 model, revealing a direct, non-first-order phase transition with unique ground state properties.

Contribution

It demonstrates the absence of a critical nematic phase near the SU(3) point and clarifies the nature of the phase transition using effective field theories and tensor network methods.

Findings

No critical nematic phase near the SU(3) point.

The phase transition is direct and not first-order.

Ground states at the transition are highly degenerate and scale-invariant.

Abstract

The absence of a critical nematic phase in the vicinity of the $\rm {SU}(3)$ ferromagnetic point for the one-dimensional spin-1 bilinear-biquadratic model is demonstrated by means of the tensor network algorithms. As it turns out, the phase transition from the ferromagnetic phase to the dimerized phase at the $\rm {SU}(3)$ ferromagnetic point is direct, but not of the first-order. The transition point features highly degenerate ground states, which are scale but not conformally invariant, with the fractal dimension being equal to 2. The conceptual developments in effective field theories - the fractal dimension and the counting rule of the Goldstone modes - play a pivotal role in clarifying the numerical artifacts arising from the finiteness of the bond dimension in the tensor network simulations, which are attributed to a proximity effect to a highly entangled scale or conformally invariant ground state.