Dicke model: entanglement as a finite size effect

TL;DR

This paper investigates how entanglement in the ground state of the Dicke model varies with system size, revealing finite-size effects that are missed by mean-field theory and are significant near the quantum phase transition.

Contribution

It demonstrates that finite systems exhibit bipartite entanglement in the ground state, which diminishes as system size increases, highlighting a non-perturbative effect overlooked by mean-field approximations.

Findings

Entanglement exists only in a narrow regime around the threshold coupling.

The size of the entangled regime scales inversely with the number of spins.

Entanglement disappears in the infinite system limit.

Abstract

We analyze 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 Bose-Einstein condensate at a threshold coupling. We show that in a finite system the spin part of the ground state is a bipartite entangled state, which can be tested by probing two parts of the spin system separately, but only in a narrow regime around the threshold coupling. Around the resonance, the size of this regime is inversely proportional to the number of spins and shrinks down to zero for infinite systems. This spin entanglement is a non-perturbative effect and is also missed by the mean-field approximation.