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

TL;DR

This paper provides an exact analytical solution for the finite size Dicke model, revealing its spectral properties, non-integrability at finite coupling, and exploring multipartite entanglement dynamics.

Contribution

It introduces a unified analytical approach to solve the finite size Dicke model and derives the G-function, spectrum, and eigenvalues, highlighting non-integrability and entanglement dynamics.

Findings

Exact spectrum obtained from zeros of the G-function

Non-integrability suggested for N>1 at finite coupling

Application to multipartite entanglement dynamics

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.