Quantum-entanglement aspects of polaron systems

TL;DR

This paper investigates the quantum entanglement in polaron ground states within coupled electron-phonon systems, revealing a nonanalyticity in entanglement entropy related to particle localization and delocalization, using variational and numerical methods.

Contribution

It introduces a combined variational and numerical approach to analyze particle-phonon entanglement in a model with local and nonlocal couplings, highlighting nonanalytic behavior without a phase transition.

Findings

Entanglement entropy shows nonanalyticity with respect to Peierls coupling.

Entanglement saturates in the self-trapped, small-polaron regime.

Particle localization correlates with increased entanglement.

Abstract

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 nonanalyticity in the entanglement entropies with respect to the Peierls-coupling strength. The occurrence of such nonanalyticity -- 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.