Spin-Wave Spectrum of the Antiferromagnetic Linear Chain

Jacques des Cloizeaux; J. J. Pearson

doi:10.1103/PhysRev.128.2131

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Spin-Wave Spectrum of the Antiferromagnetic Linear Chain

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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Phys. Rev. 128, 2131 – Published 1 December, 1962

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

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 $H = Σ j^{} S_{j} \cdot S_{j + 1}$ with periodic boundary conditions. For an infinite chain, their spectrum is $ε_{k} = (\frac{π}{2}) | sin k |$ , whereas Anderson's spin-wave theory gives $ε_{k} = | sin k |$ . 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.

References (6)

H. Bethe, Z. Physik 71, 205 (1931) in Handbuch der Physik, edited by S. Flügge (Springer Verlag, Berlin, 1933), Vol. XXIV/2, p. 604
L. Hulthén, Arkiv Mat. Astron. Fysik 26A, 1 (1938)
L. F. Mattheiss, Phys. Rev. 123, 1209 (1961)
L. F. Mattheiss[Phys. Rev. 115, 1181 (1959)]
Omitted endnote
P. W. Anderson, Phys. Rev. 86, 694 (1952)

[c1] H. Bethe, Z. Physik 71, 205 (1931) in Handbuch der Physik, edited by S. Flügge (Springer Verlag, Berlin, 1933), Vol. XXIV/2, p. 604

[c2] L. Hulthén, Arkiv Mat. Astron. Fysik 26A, 1 (1938)

[c3] L. F. Mattheiss, Phys. Rev. 123, 1209 (1961)

[c4] L. F. Mattheiss[Phys. Rev. 115, 1181 (1959)]

[c5] Omitted endnote

[c6] P. W. Anderson, Phys. Rev. 86, 694 (1952)

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Spin-Wave Spectrum of the Antiferromagnetic Linear Chain

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