Validity of spin wave theory for the quantum Heisenberg model

Abstract

Spin wave theory is a key ingredient in our comprehension of quantum spin systems, and is used successfully for understanding a wide range of magnetic phenomena, including magnon condensation and stability of patterns in dipolar systems. Nevertheless, several decades of research failed to establish the validity of spin wave theory rigorously, even for the simplest models of quantum spins. A rigorous justification of the method for the three-dimensional quantum Heisenberg ferromagnet at low temperatures is presented here. We derive sharp bounds on its free energy by combining a bosonic formulation of the model introduced by Holstein and Primakoff with probabilistic estimates and operator inequalities.

arXiv comment4 pages

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• Realization of Bose-Einstein condensation of dilute magnons in TlCuCl${}_3$
• Effects of symmetry breaking in finite quantum systems
• Phase Diagram for Magnon Condensate in Yttrium Iron Garnet Film
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Cited by in corpus (5)

• Validity of the spin-wave approximation for the free energy of the Heisenberg ferromagnet
• Computing spectral bounds of the Heisenberg ferromagnet from geometric considerations
• Magnon-Magnon Interactions in O(3) Ferromagnets and Equations of Motion for Spin Operators
• Existence of Néel order in the S=1 bilinear-biquadratic Heisenberg model via random loops
• Free energy asymptotics of the quantum Heisenberg spin chain