Distinguish the dynamical critical exponent from competing predictions

Determine whether the dynamical critical exponent at the Nahum transition is exactly z=2 or instead takes the epsilon-expansion value z\approx1.992, which cannot be resolved with the numerical accuracy available in the study.

Background

The paper investigates a critical transition between unmagnetized and magnetized Luttinger-liquid phases in a U(1)-symmetric spin-1 Heisenberg chain with biquadratic interactions. Renormalization-group calculations predict a dynamical critical exponent z\approx1.992, while the numerical finite-size scaling results are consistent with z\simeq2.

The available numerical data do not resolve the small difference between these two values. Consequently, determining the asymptotic value of z at the Nahum transition remains an unresolved issue requiring more precise numerical or analytical analysis.

References

With the available numerical accuracy it is impossible to distinguish the field-theory value $z\approx1.992$ from $z=2$.

— Criticality enabled long-range order in a U(1)-symmetric spin-1 Heisenberg chain with biquadratic interactions  (2609.31319 - Chepiga et al., 25 Sep 2026) in Subsection “Dynamical critical exponent,” Section “Vicinity of the Nahum transition”