Charge ordering in extended Hubbard models: Variational cluster approach

TL;DR

This paper extends the variational cluster perturbation theory to study charge ordering in extended Hubbard models, accurately capturing short-range correlations and revealing phase transitions in 1D and 2D systems.

Contribution

It introduces a generalized variational cluster approach for extended Hubbard models, effectively handling short-range correlations and applying it to 1D and 2D cases with new insights into phase transitions.

Findings

Accurately reproduces QMC and DMRG results in 1D.

Identifies a first-order phase transition in 2D at U>=3t.

Calculates single-particle spectral functions for both systems.

Abstract

We present a generalization of the recently proposed variational cluster perturbation theory to extended Hubbard models at half filling with repulsive nearest neighbor interaction. The method takes into account short-range correlations correctly by the exact diagonalisation of clusters of finite size, whereas long-range order beyond the size of the clusters is treated on a mean-field level. For one dimension, we show that quantum Monte Carlo and density-matrix renormalization-group results can be reproduced with very good accuracy. Moreover we apply the method to the two-dimensional extended Hubbard model on a square lattice. In contrast to the one-dimensional case, a first order phase transition between spin density wave phase and charge density wave phase is found as function of the nearest-neighbor interaction at onsite interactions U>=3t. The single-particle spectral function is calculated for both the one-dimensional and the two-dimensional system.