Validity of spin-wave theory for the quantum Heisenberg model
1 Dipartimento di Matematica e Fisica, Università di Roma Tre - L.go S. L. Murialdo 1, 00146 Roma, Italy
2 Institute of Science and Technology Austria (IST Austria) - Am Campus 1, 3400 Klosterneuburg, Austria
Received: 23 July 2014
Accepted: 29 September 2014
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.
PACS: 05.30.-d – Quantum statistical mechanics / 64.60.De – Statistical mechanics of model systems (Ising model, Potts model, field-theory models, Monte Carlo techniques, etc.) / 75.10.Jm – Quantized spin models, including quantum spin frustration
© EPLA, 2014