Spin-Wave Spectrum of the Antiferromagnetic Linear Chain

Jacques des Cloizeaux and J. J. Pearson
Phys. Rev. 128, 2131 – Published 1 December 1962
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Abstract

The methods of Bethe and Hulthén are used to build spin-wave states for the antiferromagnetic linear chain. These states, of spin 1 and translational quantum number k, are eigenstates of the Hamiltonian H=ΣjSj·Sj+1 with periodic boundary conditions. For an infinite chain, their spectrum is εk=(π2)|sink|, whereas Anderson's spin-wave theory gives εk=|sink|. For finite chains it has been verified by numerical computation that these states are the lowest states of given k, but no rigorous proof has been given for an infinite chain.

  • Received 30 July 1962

DOI:https://doi.org/10.1103/PhysRev.128.2131

©1962 American Physical Society

Authors & Affiliations

Jacques des Cloizeaux* and J. J. Pearson

  • University of California, San Diego, La Jolla, California

  • *On leave from the Centre d'Etudes Nucléaires de Saclay, Gif-sur-Yvette, France.
  • Present address: Centre d'Etudes Nucléaires de Saclay, Gif-sur-Yvette, France.

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Issue

Vol. 128, Iss. 5 — December 1962

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