Rigorous determination of spontaneously dimerized ground states in 1D Heisenberg antiferromagnets

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Abstract

Starting from the exact result of Majumdar and Ghosh (1969) for the dimerized ground state of a Heisenberg S=1/2 antiferromagnet with competing next-nearest-neighbour interaction J 2+1/2J1 on a linear chain, it is shown that this state is the ground state of the same kind of Hamiltonian, if couplings are extended up to 2n-nearest-neighbours, and the relation J1=2n, J2=2n-1, ..., J2n=1 holds. Furthermore, it is proved rigorously that this state is the ground state when n=2 and J1-2J2+J 3=0, J3=2J4, in a finite interval of values of the parameter J4. A rigorous lower limit for the extension of this interval is found to be 0<or=J4<or=1/ 4J1. A comparison with ground-state configurations of the equivalent classical Heisenberg and Ising model is discussed.

Original languageEnglish (US)
Article number008
Pages (from-to)445-453
Number of pages9
JournalJournal of Physics: Condensed Matter
Volume3
Issue number4
DOIs
StatePublished - Dec 1 1991

ASJC Scopus subject areas

  • Materials Science(all)
  • Condensed Matter Physics

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