Linear energy bounds for Heisenberg spin systems

TL;DR

This paper generalizes linear energy bounds for Heisenberg spin systems to include arbitrary spin quantum numbers and coupling schemes, expanding the class of independent magnon states with rigorously established ground-state properties.

Contribution

It extends existing linear energy bounds to more general Heisenberg models, broadening the class of states with proven ground-state properties.

Findings

Expanded class of independent magnon states

Linear energy bounds valid for arbitrary spins

Exchange matrix with constant row sums can be gauge-transformed

Abstract

Recently obtained results on linear energy bounds are generalized to arbitrary spin quantum numbers and coupling schemes. Thereby the class of so-called independent magnon states, for which the relative ground-state property can be rigorously established, is considerably enlarged. We still require that the matrix of exchange parameters has constant row sums, but this can be achieved by means of a suitable gauge and need not be considered as a physical restriction.