Capturing non-local interaction effects in the Hubbard model: optimal mappings and limits of applicability

TL;DR

This paper explores how to effectively map extended Hubbard models with nonlocal interactions to simpler local models using variational principles, assessing the accuracy and limits of these mappings through various computational methods.

Contribution

It introduces a variational approach to map nonlocal interactions to local Hubbard models and evaluates the effectiveness of different computational methods in capturing these effects.

Findings

Renormalization of local interactions by nonlocal terms quantified.

Dual boson and RPA methods provide practical approximations for real materials.

Benchmarking shows the limits of effective local models in reproducing extended Hubbard model observables.

Abstract

We investigate the Peierls-Feynman-Bogoliubov variational principle to map Hubbard models with nonlocal interactions to effective models with only local interactions. We study the renormalization of the local interaction induced by nearest-neighbor interaction and assess the quality of the effective Hubbard models in reproducing observables of the corresponding extended Hubbard models. We compare the renormalization of the local interactions as obtained from numerically exact determinant Quantum Monte Carlo to approximate but more generally applicable calculations using dual boson, dynamical mean field theory, and the random phase approximation. These more approximate approaches are crucial for any application with real materials in mind. Furthermore, we use the dual boson method to calculate observables of the extended Hubbard models directly and benchmark these against determinant Quantum Monte Carlo simulations of the effective Hubbard model.