Volume 141, Number 5, March 2023
|Number of page(s)||5|
|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: firstname.lastname@example.org (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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