Behavior of quantum entropies in polaronic systems

TL;DR

This paper investigates quantum entropies in polaronic systems with different electron-phonon interactions, revealing how these entropies behave across coupling regimes and system sizes using advanced variational methods.

Contribution

It introduces a highly accurate variational wave function to analyze quantum entropies in polaronic models with both short and long range couplings across all regimes.

Findings

Linear entropy is highly sensitive to coupling range and adiabatic ratio.

Entanglement entropy scales logarithmically with system size.

Entropies effectively characterize the crossover from weak to strong coupling.

Abstract

Quantum entropies and state distances are analyzed in polaronic systems with short range (Holstein model) and long range (Fr$\ddot{o}$hlich model) electron-phonon coupling. These quantities are extracted by a variational wave function which describes very accurately polaron systems with arbitrary size in all the relevant parameter regimes. With the use of quantum information tools, the crossover region from weak to strong coupling regime can be characterized with high precision. Then, the linear entropy is found to be very sensitive to the range of the electron-phonon coupling and the adiabatic ratio. Finally, the entanglement entropy is studied as a function of the system size pointing out that it not bounded, but scales as the logarithm of the size either for weak electron-phonon coupling or for short range interaction. This behavior is ascribed to the peculiar coupling induced by the single electron itinerant dynamics on the phonon subsystem.