Origin of rugosity sensitivity at the XXZ isotropic point

Determine whether the pronounced rugosity feature at the isotropic point [?]Delta=1 in the spin-1/2 XXZ chain is primarily associated with the enhanced SU(2) symmetry at that point or is instead a more general consequence of Berezinskii[?]Kosterlitz[?]Thouless criticality.

Background

The paper studies rugosity, a quantum-texture measure, as a probe of phase transitions in the spin-1/2 XXZ chain. The authors find a sharp rugosity peak at Delta=1, where the BKT transition coincides with the isotropic SU(2)-symmetric point of the model. They suggest that rugosity may be especially sensitive to the hierarchy of transverse spin correlations at this point.

The unresolved issue is whether the observed feature is caused specifically by the enhanced symmetry at Delta=1 or whether rugosity generally exhibits this behavior at BKT transitions, independently of the XXZ model's isotropic symmetry. The paper does not resolve this distinction.