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abstract: 'We present analytical solutions to three qubits and a single-mode cavity coupling system beyond the rotating-wave approximation (RWA). The zeroth-order approximation, equivalent to the adiabatic approximation, works well for arbitrary coupling strength for small qubit frequency. The first-order approximation, called the generalized rotating-wave approximation (GRWA), produces an effective solvable Hamiltonian with the same form as the ordinary RWA one and exhibits substantial improvements of energy levels over the RWA even on resonance. Based on these analytical eigen-solutions, we study both the bipartite entanglement and genuine multipartite entanglement (GME). The dynamics of these two kinds of entanglements using the GRWA are consistent with the numerical exact ones. Interestingly, the well-known sudden death of entanglement occurs in the bipartite entanglement dynamics but not in the GME dynamics.'
address: |
     $^{1}$Department of Physics, Chongqing University, Chongqing 401331, P. R. China\
    $^{2}$Department of Physics, Zhejiang University, Hangzhou 310027, P. R. China\
    $^{3}$ Collaborative Innovation Center of Advanced Microstructures, Nanjing 210093, China 
author:
- 'Yu-Yu Zhang$^{1,*}$, Xiang-You Chen$^{1}$, Shu He$^{2}$, Qing-Hu Chen$^{2,3,\dagger}$'
title: 'Analytical solutions and genuine multipartite entanglement of the three-qubit Dicke model'
---

Introduction
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The interaction between qubits and a cavity is ubiquitous in several branches of physics ranging from 