Spectral Functions of the Holstein Polaron: Exact and Approximate Solutions

TL;DR

This paper demonstrates that dynamical mean field theory, traditionally used in higher dimensions, provides an accurate and computationally efficient approximation for the spectral function of the Holstein model across all parameters, including in one dimension.

Contribution

It shows that dynamical mean field theory is a reliable approximation for the Holstein model's spectral function in all dimensions, validated by multiple numerical methods.

Findings

DMFT provides excellent spectral function approximation in 1D.

Comparison with hierarchical equations of motion confirms DMFT accuracy.

Results are consistent with quantum Monte Carlo and exact diagonalization.

Abstract

It is generally accepted that the dynamical mean field theory gives a good solution of the Holstein model, but only in dimensions greater than two. Here, we show that this theory, which becomes exact in the weak coupling and in the atomic limit, provides an excellent, numerically cheap, approximate solution for the spectral function of the Holstein model in the whole range of parameters, even in one dimension. To establish this, we make a detailed comparison with the spectral functions that we obtain using the newly developed momentum-space numerically exact hierarchical equations of motion method, which yields electronic correlation functions directly in real time. We crosscheck these conclusions with our path integral quantum Monte Carlo and exact diagonalization results, as well as with the available numerically exact results from the literature.