Carla Maria Pontes Carneiro

arXiv2022

Application of an inverse Holstein-Primakoff transformation to the Jaynes-Cummings model

A modification of the Holstein-Primakoff transformation is proposed such that creation and annihilation operators for a bosonic field are rewritten as operators of a $SU(2)$ algebra. Once it is applied to a quantum Hamiltonian, a subsequent application of the prescription by Lieb to obtain the classical limit for spin operators allows one to write efficiently a classical Hamiltonian for the system. This process is illustrated for the $M$-atom Jaynes-Cummings model.

quant-ph↗

arXiv2022

Analysis of quantum phase transition in some different Curie-Weiss models: a unified approach

A unified approach to the analysis of quantum phase transitions in some different Curie-Weiss models is proposed such that they are treated and analyzed under the same general scheme. This approach takes three steps: balancing the quantum Hamiltonian by an appropriate factor, rewriting the Hamiltonian in terms of $SU(2)$ operators only, and obtention of a classical Hamiltonian. $SU(2)$ operators are obtained from creation and annihilation operators as linear combinations in the case of fermions and as an inverse Holstein-Primakoff transformation in the case of bosons. This scheme is successfully applied to Lipkin, pairing, Jaynes-Cummings, bilayer, and Heisenberg models.

quant-ph↗