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

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