A cluster-based mean-field and perturbative description of strongly correlated fermion systems. Application to the 1D and 2D Hubbard model

TL;DR

This paper presents a cluster-based mean-field and perturbative method to accurately model strongly correlated fermion systems, demonstrated on 1D and 2D Hubbard models, showing promising results with large clusters or second-order perturbation.

Contribution

It introduces a novel cluster mean-field approach combined with perturbation theory for strongly correlated fermions, emphasizing basis optimization and inter-cluster correlation treatment.

Findings

Accurate ground state descriptions for Hubbard models achieved.

Second-order perturbation improves results with manageable computational effort.

Large clusters enhance the method's accuracy.

Abstract

We introduce a mean-field and perturbative approach, based on clusters, to describe the ground state of fermionic strongly-correlated systems. In cluster mean-field, the ground state wavefunction is written as a simple tensor product over optimized cluster states. The optimization of the single-particle basis where the cluster mean-field is expressed is crucial in order to obtain high-quality results. The mean-field nature of the ansatz allows us to formulate a perturbative approach to account for inter-cluster correlations; other traditional many-body strategies can be easily devised in terms of the cluster states. We present benchmark calculations on the half-filled 1D and (square) 2D Hubbard model, as well as the lightly-doped regime in 2D, using cluster mean-field and second-order perturbation theory. Our results indicate that, with sufficiently large clusters or to second-order in perturbation theory, a cluster-based approach can provide an accurate description of the Hubbard model in the considered regimes. Several avenues to improve upon the results presented in this work are discussed.