Approximating parabolas as natural bounds of Heisenberg spectra: Reply on the comment of O. Waldmann

TL;DR

This paper discusses how, under specific conditions, parabola-shaped bounds derived from spin coherent states can effectively approximate the spectra of certain spin systems, addressing previous inaccuracies in quadratic approximations.

Contribution

It introduces a new perspective that parabola bounds from spin coherent states serve as natural spectrum bounds, refining prior quadratic approximation methods.

Findings

Parabolas can serve as natural bounds for spin system spectra.

Quadratic approximations may poorly estimate extremal energies.

Spin coherent states provide a basis for these bounds.

Abstract

O. Waldmann has shown that some spin systems, which fulfill the condition of a weakly homogeneous coupling matrix, have a spectrum whose minimal or maximal energies are rather poorly approximated by a quadratic dependence on the total spin quantum number. We comment on this observation and provide the new argument that, under certain conditions, the approximating parabolas appear as natural bounds of the spectrum generated by spin coherent states.