Structure and relevant dimension of the Heisenberg model and applications to spin rings

TL;DR

This paper analyzes the structure and relevant dimensions of the Heisenberg model, providing formulas and results for symmetric systems, especially spin rings, using magnon states and identifying solvable cases.

Contribution

It introduces general formulas for relevant dimensions in the Heisenberg model and applies them to spin rings, including analytical solutions for small systems.

Findings

Formulas for relevant dimensions depending on symmetries

Diagonalization results for spin rings using magnon states

Identification of analytically solvable small spin rings

Abstract

For the diagonalization of the Hamilton matrix in the Heisenberg model relevant dimensions are determined depending on the applicable symmetries. Results are presented, both, by general formulae in closed form and by the respective numbers for a variety of special systems. In the case of cyclic symmetry, diagonalizations for Heisenberg spin rings are performed with the use of so-called magnon states. Analytically solvable cases of small spin rings are singled out and evaluated.