FM 07-14 (arXiv:1404.4717)

Authors: M. Correggi, A. Giuliani, R. Seiringer

Title: 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.

Keywords: Quantum Heisenberg ferromagnet, 3D quantum spins, spin-wave theory, localization bounds, Holstein-Primakoff representation, random walk representation, functional inequalitites.

M. Correggi
Dipartimento di Matematica e Fisica, Università di Roma Tre
E-mail address: michele DOT correggi AT gmail DOT com

A. Giuliani
Dipartimento di Matematica e Fisica, Università di Roma Tre
E-mail address: giuliani AT mat DOT uniroma3 DOT it

R. Seiringer
IST Austria
E-mail address: robert DOT seiringer AT ist DOT ac DOT at