Finite-size scaling analysis in the two-photon Dicke model

TL;DR

This paper performs a finite-size scaling analysis of the two-photon Dicke model, revealing critical behavior and phase transition characteristics beyond mean-field approximations, with analytical derivation of scaling exponents.

Contribution

It introduces a finite-size scaling analysis for the two-photon Dicke model and derives universal scaling exponents analytically.

Findings

Spectral collapse observed in the model.

Super-radiant phase transition characterized by vanishing excitation energy.

Scaling exponents match those of the one-photon Dicke model.

Abstract

The Hamiltonian of the two-photon Dicke model is diagonalized for the normal phase and super-radiant phase beyond the mean-field method respectively, giving the critical coupling strength. Besides a spectral collapse, the super-radiant phase transition is presented by the vanishing of the excitation energy, which is lower than the mean-field results. Finite-size scaling exponents for the ground-state energy and the atomic angular momentum are analytically derived from scaling hypothesis, belonging to the same scaling universality of the one-photon Dicke model.