# Quantum phase transition in an effective three-mode model of interacting bosons. (arXiv:1801.05866v1 [quant-ph])

In this work we study an effective three-mode model describing interacting

bosons. These bosons can be considered as exciton-polaritons in a semiconductor

microcavity at the magic angle. This model exhibits quantum phase transition

(QPT) when the parameters of the corresponding Hamiltonian are continuously

varied. The properties of the Hamiltonian spectrum (e.g., the distance between

two adjacent energy levels) and the phase space structure of the thermodynamic

limit of the model are used to indicate QPT. The relation between spectral

properties of the Hamiltonian and the corresponding classical frame of the

thermodynamic limit of the model is established as indicative of QPT . The

average number of bosons in a specific mode and the entanglement properties of

the ground state as functions of the parameters are used to characterize the

order of the transition and also to construct a phase diagram. Finally, we

verify our results for experimental data obtained for a setting of

exciton-polaritons in a semiconductor microcavity.