Exact solvability, non-integrability, and genuine multipartite entanglement dynamics of the Dicke model

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.

18 pages, 5 figures

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Cited by in corpus (3)

• The quantum Rabi model: solution and dynamics
• Algebraic structure of the two-qubit quantum Rabi model and its solvability using Bogoliubov operators
• A transition in the spectral statistics of quantum optical model by different electromagnetic fields