A Ferromagnetic Lieb-Mattis Theorem

Abstract

We prove ferromagnetic ordering of energy levels for XXX Heisenberg chains of any spin and XXZ spin chains with all spins equal to 1/2. Ferromagnetic ordering means that the minimum energies in the invariant subspaces of fixed total spin are monotone decreasing as a function of the total spin. This result provides a ferromagnetic analogue of the well-known theorem by Lieb and Mattis about ordering of energy levels in antiferromagnetic and ferrimagnetic systems on bipartite graphs.

4 pages, final version, some references added

References in corpus (3)

• Lieb-Schultz-Mattis in Higher Dimensions
• Droplet States in the XXZ Heisenberg Chain
• Ferromagnetic Ordering of Energy Levels

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