Momentum average approximation for models with electron-phonon coupling dependent on the phonon momentum

TL;DR

This paper extends the momentum average approximation to models with momentum-dependent electron-phonon interactions, providing an analytical, accurate, and computationally simple method validated against numerical data and improved via variational techniques.

Contribution

The authors develop a generalized momentum average approximation for momentum-dependent electron-phonon models, enhancing accuracy and applicability over previous methods.

Findings

Analytical expressions are accurate across parameter space.

Validation against numerical data confirms high accuracy.

Variational improvements reduce errors to within 0.3%.

Abstract

We generalize the momentum average (MA) approximation to study the properties of models with momentum-dependent electron-phonon coupling. As in the case of the application of the original MA to the Holstein model, the results are analytical, numerically trivial to evaluate, exact for both zero bandwidth and for zero electron-phonon coupling, and are accurate everywhere in parameter space. Comparison with available numerical data confirms this accuracy. We then show that further improvements can be obtained based on variational considerations, using the one-dimensional breathing-mode Hamiltonian as a specific example. For example, by using this variational MA, we obtain ground state energies within at most 0.3% error of the numerical data.