Polarons and slow quantum phonons

TL;DR

This paper presents an improved numerical study of Holstein polarons across all regimes, focusing on their mass, radius, and transport properties, with implications for broader models.

Contribution

It introduces an enhanced variational diagonalization method to accurately analyze polaron properties, including in the strong coupling adiabatic regime.

Findings

Large and heavy adiabatic polarons can form.

Polaron mass behavior varies between 1D and 3D.

Transport properties are characterized by optical conductivity and sum rules.

Abstract

We describe the formation and properties of Holstein polarons in the entire parameter regime. Our presentation focuses on the polaron mass and radius, which we obtain with an improved numerical technique. It is based on the combination of variational exact diagonalization with an improved construction of phonon states, providing results even for the strong coupling adiabatic regime. In particular we can describe the formation of large and heavy adiabatic polarons. A comparison of the polaron mass for the one and three dimensional situation explains how the different properties in the static oscillator limit determine the behavior in the adiabatic regime. The transport properties of large and small polarons are characterized by the f-sum rule and the optical conductivity. Our calculations are approximation-free and have negligible numerical error. This allows us to give a conclusive and impartial description of polaron formation. We finally discuss the implications of our results for situations beyond the Holstein model.