Exact solvability, non-integrability, and genuine multipartite entanglement dynamics of the Dicke model (1404.7834v2)

Abstract: In this paper, the finite size Dicke model of arbitrary number of qubits is solved analytically in an unified way within extended coherent states. For the $N=2k$ or $2k-1$ Dicke models ($k$ is an integer), the $G$-function, which is only an energy dependent $k \times k$ determinant, is derived in a transparent manner. The regular spectrum is completely and uniquely given by stable zeros of the $G$-function. The closed-form exceptional eigenvalues are also derived. The level distribution controlled by the pole structure of the $G$-functions suggests non-integrability for $N>1$ model at any finite coupling in the sense of recent criterion in literature. A preliminary application to the exact dynamics of genuine multipartite entanglement in the finite $N$ Dicke model is presented using the obtained exact solutions.