Singularity with and without disorder at AKLT points

TL;DR

This paper investigates the nature of AKLT points in spin chains, revealing that in certain SU(N) models, these points are not disorder points despite exhibiting singular wave vectors, contrasting with traditional AKLT behavior.

Contribution

It demonstrates that AKLT points can occur within incommensurate phases without being disorder points in non-self-conjugate SU(N) models, expanding understanding of their properties.

Findings

AKLT points are not always disorder points in SU(N) models.

Wave vectors remain singular on both sides of the AKLT point in certain models.

Self-conjugate representations retain the disorder point nature of AKLT points.

Abstract

The Affleck-Kennedy-Lieb-Tasaki (AKLT) point of the bilinear-biquadratic spin-1 chain is a cornerstone example of a disorder point where short-range correlations become incommensurate, and correlation lengths and momenta are non-analytic. While the presence of singularities appears to be generic for AKLT points, we show that for a family of SU(N) models, the AKLT point is not a disorder point: It occurs entirely within an incommensurate phase yet the wave vector remains singular on both sides of the AKLT point. We conjecture that this new possibility is generic for models where the representation is not self-conjugate and the transfer matrix non-Hermitian, while for self-conjugate representations the AKLT points remain disorder points.