# Competition between antiferromagnetic and charge density wave fluctuations in the extended Hubbard model

## TL;DR

This study uses an advanced parquet approach to analyze the competition between charge and spin fluctuations in the extended Hubbard model, revealing that antiferromagnetic fluctuations dominate except near the charge density wave transition.

## Contribution

It extends the parquet method to include non-local Coulomb interactions, providing a comprehensive analysis of fluctuation competition in the extended Hubbard model.

## Key findings

- Charge and spin fluctuation competition is narrow near the phase transition.
- Antiferromagnetic fluctuations dominate due to lattice geometry.
- Multiple observables consistently support the conclusions.

## Abstract

By extending our {\it victory} implementation of the parquet approach to include non-local Coulomb interactions, we study the extended Hubbard model on the two-dimensional square lattice with a particular focus on the competition of the non-local charge and spin fluctuations. Surprisingly, we find that their competition, as the mechanism driving the phase transition towards the charge density wave, dominates only in a very narrow parameter regime in the immediate vicinity of the phase transition. Due to the special geometry and the Fermi surface topology of the square lattice, antiferromagnetic fluctuations dominate even for sizable next-nearest neighbor interactions. Our conclusions are based on the consistent observations in both the single- and two- particle quantities, including the self-energy, the single-particle spectral function, the two-particle susceptibility, the density-density vertex function and the optical conductivity. Our work unbiasedly establishes the connection of these quantities to the charge fluctuations, and the way of interpretation can be readily applied to any many-body method with access to the two-particle vertex.