On the Ground State of Ferromagnetic Hamiltonians

TL;DR

This paper rigorously proves that the ground state of ferromagnetic Heisenberg-Dirac-Van Vleck Hamiltonians on s=1/2 spins always has maximal total spin, regardless of lattice structure or dimension.

Contribution

It provides a lattice- and topology-independent proof confirming the maximal total spin of the ground state in ferromagnetic Hamiltonians.

Findings

Ground state has maximal total spin S=N/2.

Ground state is (N+1)-fold degenerate.

Proof applies regardless of lattice dimension or topology.

Abstract

It is generally believed that the ground state of the ferromagnetic Heisenberg-Dirac-Van Vleck Hamiltonians acting on s=1/2 spins of a lattice with N sites has the maximal possible value of the total spin S=N/2 and is N+1 times degenerate. We present a rigorous proof of this statement, independent of the lattice dimension and topology.