A Ferromagnetic Lieb-Mattis Theorem

Details A Ferromagnetic Lieb-Mattis Theorem A Ferromagnetic Lieb-Mattis Theorem

2004-08-11

arxiv.org/abs/math-ph/0408020v3

Phys. Rev. Lett., 94 (2005) 057206

Physics

Mathematical Physics

4 pages, final version, some references added

Scientific paper

10.1103/PhysRevLett.94.057206

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.

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