Holstein polaron: the effect of multiple phonon modes

TL;DR

This paper extends the Momentum Average approximation to analyze how multiple optical phonon modes influence the properties of a Holstein polaron, revealing cumulative effects on ground state and significant impacts on higher energy spectra.

Contribution

It introduces a generalized MA approximation for multiple phonon modes, providing a computationally efficient and accurate method for studying complex polaron systems.

Findings

Ground-state properties are cumulatively affected by multiple phonon modes.

A dominant mode determines the ground-state characteristics.

Weak coupling to additional modes significantly alters high-energy spectral features.

Abstract

We generalize the Momentum Average approximations MA$^{(0)}$ and MA$^{(1)}$ to study the effects of coupling to multiple optical phonons on the properties of a Holstein polaron. As for a single phonon mode, these approximations are numerically very efficient. They become exact for very weak or very strong couplings, and are highly accurate in the intermediate regimes, {\em e.g.} the spectral weights obey exactly the first six, respectively eight, sum rules. Our results show that the effect on ground-state properties is cumulative in nature. In particular, if the effective coupling to one mode is much larger than to the others, this mode effectively determines the GS properties. However, even very weak coupling to a second phonon mode has important non-perturbational effects on the higher energy spectrum, in particular on the dispersion and the phonon statistics of the polaron band.