Quantum many-body states and Green functions of nonequilibrium electron-magnon systems: Localized spin operators vs. their mapping to Holstein-Primakoff bosons

Abstract

The operators of localized spins within a magnetic material commute at different sites of its lattice and anticommute on the same site, so they are neither fermionic nor bosonic operators. Thus, to construct diagrammatic many-body perturbation theory, the spin operators are usually mapped to the bosonic ones with Holstein-Primakoff (HP) transformation being the most widely used in magnonics and spintronics literature. However, to make calculations tractable, the square root of operators in the HP transformation is expanded into a Taylor series truncated to some low order. This poses a question on the range of validity of truncated HP transformation when describing nonequilibrium dynamics of localized spins interacting with each other or with conduction electron spins. Here we apply exact diagonalization techniques to Hamiltonian of fermions (i.e., electrons) interacting with HP bosons vs. Hamiltonian of fermions interacting with the original localized spin operators in order to compare their many-body states and one-particle equilibrium or nonequilibrium Green functions. The Hamiltonian of fermions interacting with HP bosons gives incorrect ground state and electronic spectral function, unless large number of terms are retained in truncated HP transformation. Furthermore, tracking nonequilibrium dynamics of localized spins over longer time intervals requires progressively larger number of terms in truncated HP transformation. Finally, we show that recently proposed [M. Vogl et al., Phys. Rev. Research 2, 043243 (2020); J. König et al., SciPost Phys. 10, 007 (2021)] resummed HP transformation resolves the trouble with truncated HP transformation, while allowing us to derive an exact (manifestly Hermitian) Hamiltonian consisting of finite and fixed number of boson-boson and electron-boson interacting terms.

23 pages, 10 figures

References in corpus (18)

• Spin Transfer Torques
• Real time evolution using the density matrix renormalization group
• Inelastic transport theory from first-principles: methodology and applications for nanoscale devices
• Spontaneous Magnon Decays
• Spin-Torque Driven Magnetization Dynamics: Micromagnetic Modelling
• Non-existence of the Luttinger-Ward functional and misleading convergence of skeleton diagrammatic series for Hubbard-like models
• Resources of nonlinear cavity magnonics for quantum information
• Stability of Bose Einstein condensates of hot magnons in YIG
• On the dangers of partial diagrammatic summations: Benchmarks for the two-dimensional Hubbard model in the weak-coupling regime
• Analytical Continuation of Matrix-Valued Functions: Carathéodory Formalism
• Exploring the limits of the self consistent Born approximation for inelastic electronic transport
• Magnon antibunching in a nanomagnet
• Green's function formalism for spin transport in metal-insulator-metal heterostructures
• Multi-scale modelling of current-induced switching in magnetic tunnel junctions using ab initio spin transfer torques
• Prethermalization from a low-density Holstein-Primakoff expansion
• Exact functionals for correlated electron-photon systems
• Chiral Spin Order in Kondo-Heisenberg systems
• Spin Transport in Quantum Spin-Orbital Liquids

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