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Phys. Rev. B 40, 4621–4626 (1989)

Spectrum of the biquadratic spin-1 antiferromagnetic chain

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Michael N. Barber
Department of Mathematics and Centre for Mathematical Analysis, School of Mathematical Sciences, Australian National University, GPO Box 4, Canberra, Australian Capital Territory 2601, Australia

Murray T. Batchelor
Department of Mathematics, University of Melbourne, Parkville, Victoria 3052, Australia
Centre for Mathematical Analysis, School of Mathematical Sciences, Australian National University, GPO Box 4, Canberra, Australian Capital Territory 2601, Australia

Received 13 March 1989; published in the issue dated 1 September 1989

An exact correspondence between the staggered biquadratic spin-1 antiferromagnetic chain and the quantum Hamiltonian limit of the nine-state Potts model is established for finite chains with free ends. For uniform interactions this equivalence is used (via a further exact mapping to a Bethe ansatz soluble XXZ model) to calculate exactly the infinite lattice values of the ground-state energy per site and the (nonzero) gap to the lowest-energy excited state. Periodic boundary conditions and the nature of the ground state as a function of bond alternation are also discussed.

© 1989 The American Physical Society

URL:
http://link.aps.org/doi/10.1103/PhysRevB.40.4621
DOI:
10.1103/PhysRevB.40.4621
PACS:
75.10.Jm, 05.30.-d, 64.60.Fr, 75.40.Cx
 
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