Numerically exact solution to the finite-size Dicke model

Dicke model: Entanglement as a finite size effect

We analyze the Dicke model at zero temperature by matrix diagonalization to determine the entanglement in the ground state. In the infinite system limit the mean field approximation predicts a quantum phase transition from a non-interacting state to a BoseEinstein condensate at a threshold coupling. We show that in a finite system the spin part of the ground state is a bipartite entangled state...

An exact Solution for a Finite Solution Server Model

Exact Finite-Size-Scaling Corrections to the Critical Two-Dimensional Ising Model on a Torus

We analyze the finite-size corrections to the energy and specific heat of the critical two-dimensional spin-1/2 Ising model on a torus. We extend the analysis of Ferdinand and Fisher to compute the correction of order L−3 to the energy and the corrections of order L−2 and L−3 to the specific heat. We also obtain general results on the form of the finite-size corrections to these quantities: onl...

An exact sampling formula for the Wright-Fisher model and a solution to a conjecture about the finite-island model.

An exact sampling formula for a Wright-Fisher population of fixed size N under the infinitely many neutral alleles model is deduced. This extends the Ewens formula for the configuration of a random sample to the case where the sample is drawn from a population of small size, that is, without the usual large-N and small-mutation-rate assumption. The formula is used to prove a conjecture ascertai...

The Dicke model in quantum optics: Dicke model revisited.

A short review of recent developments of the Dicke model in quantum optics is presented. The focus is on the model in a cavity at zero temperature and in the rotating wave approximation. Topics discussed include spectroscopic structures, the giant quantum oscillator, entanglement and phase transitions.