Projected Holstein-Primakoff boson representation of quantum spins for spin wave theory

Abstract

The Holstein-Primakoff boson representation of quantum spins and associated large-$S$ 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 $S$. We will present the exact normal-ordered forms of the finite-$S$ 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.

13 pages, 2 figures, 1 table

References in corpus (18)

• Quantum Spin Liquid States
• Linear spin wave theory for single-Q incommensurate magnetic structures
• Finite-Size Scaling of the Ground State Parameters of the Two-Dimensional Heisenberg Model
• Nematic order in square lattice frustrated ferromagnets
• Spontaneous Magnon Decays
• Magnon pairing in quantum spin nematic
• Phase diagram of spin-1/2 J1-J2 Heisenberg model on honeycomb lattice
• Weak plaquette valence bond order in the $S=1/2$ honeycomb $J_1-J_2$ Heisenberg model
• Observation of a 500meV Collective Mode in La${}_{2-x}$Sr${}_x$CuO${}_4$ and Nd${}_2$CuO${}_4$
• First order transition between magnetic order and valence-bond order in a 2D frustrated Heisenberg model
• Phase Diagram of the J1, J2, J3 Heisenberg Models on the Honeycomb Lattice: A Series Expansion Study
• Pseudo-Goldstone gaps and order-by-quantum-disorder in frustrated magnets
• Further Series Studies of the Spin-1/2 Heisenberg Antiferromagnet at T=0: Magnon Dispersion and Structure Factors
• Nematic phase and phase separation near saturation field in frustrated ferromagnets
• Magnetic excitations of the field induced states in BaCo2(AsO4)2 probed by time-domain terahertz spectroscopy
• Exact resummation of the Holstein-Primakoff expansion and differential equation approach to operator square-roots
• Schwinger boson symmetric spin liquids of Shastry-Sutherland model
• High-accuracy evaluation of non-thermal magnetic states beyond spin-wave theory: applications to higher-energy states