Ordering energy levels of interacting spin systems

Elliott Lieb, Daniel Mattis

Research output: Contribution to journalArticle

645 Scopus citations

Abstract

The total spin S is a good quantum number in problems of interacting spins. We have shown that for rather general antiferromagnetic or ferrimagnetic Hamiltonians, which need not exhibit translational invariance, the lowest energy eigenvalue for each value of S [denoted E(S)] is ordered in a natural way. In antiferromagnetism, E(S + 1) > E(S) for S ≥ 0. In ferrimagnetism, E(S + 1) > E(S) for S ≥ script S sign, and in addition the ground state belongs to S ≤ script S sign. script S sign is defined as follows: Let the maximum spin of the A sublattice be SA and of the B sublattice SB; then script S sign ≡ |SA - SB|. Antiferromagnetism is treated as the special case of script S sign = 0. We also briefly discuss the structure of the lowest eigenfunctions in an external magnetic field.

Original languageEnglish (US)
Pages (from-to)749-751
Number of pages3
JournalJournal of Mathematical Physics
Volume3
Issue number4
DOIs
StatePublished - Jan 1 1962
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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