| Issue |
EPL
Volume 141, Number 5, March 2023
|
|
|---|---|---|
| Article Number | 50002 | |
| Number of page(s) | 5 | |
| Section | General physics | |
| DOI | https://doi.org/10.1209/0295-5075/acbed8 | |
| Published online | 08 March 2023 | |
Inverse Holstein-Primakoff transformation of bosonic operators —Application to a bilayer model
1 Centro Federal de Educação Tecnológica de Minas Gerais, Programa de Pós-graduação em Modelagem Matemática e Computacional - Belo Horizonte, MG, Brazil
2 Centro Federal de Educação Tecnológica de Minas Gerais, Departamento de Matemática Belo Horizonte, MG, Brazil
(a) E-mail: giancarloqpellegrino@cefetmg.br (corresponding author)
Received: 14 December 2022
Accepted: 24 February 2023
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.
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