Ferromagnetic Ordering of Energy Levels

摘要: We study a natural conjecture regarding ferromagnetic ordering of energy levels in the Heisenberg model which complements Lieb–Mattis Theorem 1962 for antiferromagnets: models lowest energies each subspace fixed total spin are strictly ordered according to spin, with lowest, i.e., ground state, belonging maximal subspace. Our main result is proof this spin-1/2 XXX and XXZ ferromagnets one dimension. has two ingredients. The first an extension Koma Nachtergaele shows that monotonicity as function follows from state length chain. For second part we use Temperley–Lieb algebra calculate, suitable basis, matrix elements Hamiltonian restricted highest weight vectors given spin. then show positivity properties these imply necessary volume. method also excited ferromagnet on any finite tree less than