## Abstract

We give an explicit proof that the completely dimerized ('Kekulè or nearest-neighbor resonant valence bond) state is the degenerate ground state of a linear chain S =1/2 Heisenberg antiferromagnet, with competing couplings extending up to 2n nearest neighbors, if the relation J_{1} = 2n, J _{2} = 2n - 1,.,J_{2n} = 1, holds between the various exchange integrals. The previously known result for J_{2} =1/2 J_{1} is then just a special case corresponding to n=1. We study in detail n=2 (fourth-nearest neighbors) and show that this state is the ground state of the Hamiltonian when J_{1} - 2J_{2} + J_{3} = 0, J _{3} = 2J_{4}, in a finite interval of values of the parameter J_{4}. A rigorous lower limit for the extension of this interval is found to be 0 ≤ J_{4} ≤1/4 J_{1}. A comparison with ground-state configurations of the equivalent classical Heisenberg and Ising models is made.

Original language | English (US) |
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Pages (from-to) | 5813-5814 |

Number of pages | 2 |

Journal | Journal of Applied Physics |

Volume | 69 |

Issue number | 8 |

DOIs | |

State | Published - Dec 1 1991 |

## ASJC Scopus subject areas

- Physics and Astronomy(all)