# Characterization of the quantum phase transition in a two-mode Dicke model for different cooperation numbers

## TL;DR

This paper investigates how the cooperation number influences quantum phase transitions in a multi-mode Dicke model, using variational states to analyze ground state properties and entanglement.

## Contribution

It introduces the cooperation number as a key parameter and studies its effect on phase transitions and system observables in the Dicke model.

## Key findings

- Cooperation number significantly affects quantum phase transition behavior.
- Variational states provide accurate approximations of the ground state.
- Entanglement entropy varies with energy difference and coupling strength.

## Abstract

We show how the use of variational states to approximate the ground state of a system can be employed to study a multi-mode Dicke model. One of the main contributions of this work is the introduction of a not very commonly used quantity, the cooperation number, and the study of its influence on the behavior of the system, paying particular attention to the quantum phase transitions and the accuracy of the used approximations. We also show how these phase transitions affect the dependence of the expectation values of some of the observables relevant to the system and the entropy of entanglement with respect to the energy difference between atomic states and the coupling strength between matter and radiation, thus characterizing the transitions in different ways.