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

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