The Self-Trapping Line of the Holstein Molecular Crystal Model in One Dimension

TL;DR

This paper investigates the ground state of the one-dimensional Holstein model, identifying a precise self-trapping transition between small and large polaron states using a variational method.

Contribution

It introduces a robust variational approach to accurately locate the self-trapping transition in the Holstein model's parameter space.

Findings

A unique curve accurately marks the self-trapping transition.

The method effectively distinguishes small and large polaron regimes.

Energy components are analyzed across the transition.

Abstract

The ground state of the Holstein molecular crystal model in one dimension is studied using the Global-Local variational method, analyzing in particular the total energy, kinetic energy, phonon energy, and interaction energy over a broad region of the polaron parameter space. Through the application of objective criteria, a unique curve is identified that simply, accurately, and robustly locates the self-trapping transition separating small polaron and large polaron behavior.