Electronic Kinetic Energy in the Polaron Ground State and the Location of the Self-Trapping Transition

TL;DR

This paper investigates the electronic kinetic energy in the Holstein polaron model's ground state, using variational and perturbation methods to precisely locate the self-trapping transition and map the polaron phase diagram.

Contribution

It introduces a combined variational and perturbative approach to accurately identify the self-trapping transition in the Holstein model.

Findings

Precisely locates the self-trapping transition line.

Maps the polaron phase diagram distinguishing small and large polarons.

Analyzes kinetic energy across a broad parameter space.

Abstract

In this paper we discuss the electronic kinetic energy in the ground state of the Holstein Hamiltonian in one space dimension using the Global-Local variational method together with perturbation theory at weak and strong coupling. The electronic kinetic energy is detailed over a broad region of the polaron parameter space, and is analyzed to accurately determine the location of the self-trapping transition. The self-trapping line so determined separates the small polaron regime from the large polaron regime, constituting a polaron phase diagram.