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 a unifiedwaywithin extended coherent states. For the N = 2k or 2k ? 1Dickemodels (k is an integer), the G-function,which is only an energy dependent k × 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 > 1model at any finite coupling in the sense of recent criteria found in the literature. Apreliminary application to the exact dynamics of genuine multipartite entanglement in the finite-N Dicke model is presented using the obtained exact solutions.