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On an Analytic Expression for the One-Magnon Dispersion Relation in a Heisenberg Antiferromagnet

1994; Institute of Physics; Volume: 27; Issue: 5 Linguagem: Inglês

10.1209/0295-5075/27/5/011

1286-4854

Péter Krüger, P. Schuck,

Quantum many-body systems

Using the Dyson-equation approach to spin-spin correlation functions we derive self-consistent mean-field equations for the antiferromagnetic spin-(1/2) Heisenberg model. An analytic expression for the one-magnon dispersion valid in D = 1, 2, 3 is obtained. For the linear chain it gives the exact result ωk = (π/2) |sin k| known from the Bethe ansatz. For the square lattice the same procedure leads to ωk = 1.188 × 2 √1 - ((cos kx + cos ky)/2)2 in agreement with recent Monte Carlo results. Values for the simple cubic lattice in three dimensions are also given.