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

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.

22 pages, 21 figures

References in corpus (5)

• Hierarchical mean-field approach to the $J_1$-$J_2$ Heisenberg model on a square lattice
• Active space decomposition with multiple sites: Density matrix renormalization group algorithm
• Numerical Contractor Renormalization Method for Quantum Spin Models
• Variational description of the ground state of the repulsive two-dimensional Hubbard model in terms of nonorthogonal symmetry-projected Slater determinants
• Composite fermion-boson mapping for fermionic lattice models

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