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 J1 = 2n, J 2 = 2n - 1,.,J2n = 1, holds between the various exchange integrals. The previously known result for J2 =1/2 J1 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 J1 - 2J2 + J3 = 0, J 3 = 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 ≤ J4 ≤1/4 J1. A comparison with ground-state configurations of the equivalent classical Heisenberg and Ising models is made.
ASJC Scopus subject areas
- Physics and Astronomy(all)