Quantum-entanglement aspects of polaron systems

We describe quantum entanglement inherent to the polaron ground states of coupled electron-phonon (or, more generally, particle- phonon) systems based on a model comprising both local (Holstein-type) and nonlocal (Peierls-type) coupling. We study this model using a variational method supplemented by the exact numerical diagonalization on a system of finite size. By way of subsequent numerical diagonalization of the reduced density matrix, we determine the particle-phonon entanglement as given by the von Neumann and linear entropies. Our results are strongly indicative of the intimate relationship between the particle localization/delocalization and the particle-phonon entanglement. In particular, we find a compelling evidence for the existence of a non-analyticity in the entanglement entropies with respect to the Peierls-coupling strength. The occurrence of such non-analyticity -- not accompanied by an actual quantum phase transition -- reinforces analogous conclusion drawn in several recent studies of entanglement in the realm of quantum- dissipative systems. In addition, we demonstrate that the entanglement entropies saturate inside the self-trapped region where the small-polaron states are nearly maximally mixed.