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Physical review. B, Condensed matter

Holstein-Primakoff theory for many-body systems

Lawrence R. Mead, N. Papanicolaou

Published Aug 1, 1983• 35 citations
Publisher

Abstract

We discuss the relationship between generalized coherent states and suitable extensions of the Holstein-Primakoff theory of quantum spin systems, illustrating the common origin of a variety of semiclassical approximation schemes encountered in many-body theory.
DOI
10.1103/physrevb.28.1633

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The Holstein-Primakoff boson representation of quantum spins and associated large-SSS expansion have been the standard framework for describing the spin wave excitations in magnetically order phases of quantum spin systems. However, we will show that the omission of projection operators and normal-ordering in this representation can produce incorrect magnon hamiltonians for finite SSS. We will present the exact normal-ordered forms of the finite-SSS projection operators and projected Holstein-Primakoff boson representations of spin and quadrupole operators, which can produce exact two-magnon interaction terms under ferromagnetic or fully polarized states. We will also discuss the difficulties of applying this projected representation to antiferromagnetic spin wave theory.