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

Abstract

Abstract 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.