A new variational approach for the Holstein Molecular Crystal Model

TL;DR

This paper introduces a new variational method for analyzing polarons in the Holstein model, accurately capturing intermediate coupling regimes with minimal computational effort.

Contribution

It develops a superposition-based variational approach that effectively describes polaron features across different regimes and dimensions.

Findings

Accurately computes ground state energies in 1D and 2D

Provides detailed band structure and spectral properties

Requires minimal computational resources

Abstract

A new variational technique is developed to investigate the polaronic features of the Holstein Molecular Crystal Model. It is based on a linear superposition of Bloch states that describe large and small polaron wave functions. It is shown that this method provides a very good description of the regime characterized by intermediate values of the electron-phonon coupling constant (the so-called intermediate polaron) for any value of the adiabatic parameter $\omega_0/t$. The polaron ground state energy in one and two dimensions is calculated and successfully compared with the best estimates available providing a clear physical interpretation of the intermediate polaron. The band structure, the spectral weight of the ground state and the lattice displacement associated to the polaron are also calculated and discussed. The new method has the advantage to require a very little computational effort.