Inverse Holstein-Primakoff transformation of bosonic operators —Application to a bilayer model

An inversion of the Holstein-Primakoff transformation is proposed such that creation and annihilation operators for a bosonic field are rewritten as operators of an SU (2) algebra. In association with more common quadratic combinations for fermionic operators, that inverse transformation sets a quan...

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Bibliographic Details
Published in:Europhysics letters 2023-03, Vol.141 (5), p.50002
Main Authors: Pontes Carneiro, Carla Maria, Queiroz Pellegrino, Giancarlo
Format: Article
Language:English
Subjects:
Boson fields
Electron spin
Excitons
Hamiltonian functions
Holes (electron deficiencies)
Operators (mathematics)
Phase transitions
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Summary:An inversion of the Holstein-Primakoff transformation is proposed such that creation and annihilation operators for a bosonic field are rewritten as operators of an SU (2) algebra. In association with more common quadratic combinations for fermionic operators, that inverse transformation sets a quantum Hamiltonian fully in terms of SU (2) operators. A subsequent application of the prescription by Lieb, to obtain the classical limit for spin operators, then allows one to write effciently a classical Hamiltonian for the system. This process is illustrated for a bilayer model undergoing an (electron-hole)-to-exciton quantum phase transition.
ISSN:0295-5075
1286-4854
DOI:10.1209/0295-5075/acbed8