Exact solutions of an extended Dicke model

Shu He, Liwei Duan, Qing‐Hu Chen

In this paper, the finite-size Dicke model of arbitrary number of qubits is solved analytically in a unified way within extended coherent states. For the or Dicke models ( k is an integer), the G -function, which is only an energy dependent 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 model at any finite coupling in the sense of recent criteria found in the 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.

Reinhard Honegger

Qing‐Hu Chen, Yuyu Zhang, Tao Liu +1 more

By using extended bosonic coherent states, a technique to solve the Dicke model exactly is proposed in the numerical sense. The accessible system size is two orders of magnitude higher than that reported in the literature. Finite-size scaling for several observables, such as the ground-state energy, Berry phase, and concurrence, is analyzed. A scaling exponent for ground-state energy is found. An existing discrepancy in the scaling exponent of the concurrence is reconciled.

S. M. Chumakov, M. Kozierowski, A. A. Mamedov

M. Aparicio Alcalde, B. M. Pimentel

Jorge G Hirsch, M. A. Bastarrachea-Magnani

An extended bosonic coherent basis has been shown by Chen et al to provide numerically exact solutions of the finite-size Dicke model. The advantages in employing this basis, as compared with the photon number (Fock) basis, are exhibited to be valid for a large region of the Hamiltonian parameter space and many excited states by analyzing the convergence in the wave functions.