"Lattice density functional theory : Numerical correlation-energy functional
for the generalized Hubbard model"
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We present an accurate method to determine ground-state properties
of strongly-correlated electrons decribed by lattice-model Hamiltonians.
In lattice density-functional theory (LDFT) the basic variable is the
one-particle density matrix $\gamma$. From the HK theorem,
the ground state Energy $E_{gs}[\gamma_{gs}] = \min_{\gamma} E[\gamma]$
is obtained by minimizing the energy over all the representable $\gamma$. 
The energy functional can be divided into two contributions:
the kinetic-energy functional, which linear dependence on $\gamma$ is
axactly known, and the correlation-energy functional $W[\gamma]$,
which approximation constitutes the actual challenge.
Within the framework of LDFT, we develope a numerical approach to
$W[\gamma]$, which involves the exact diagonalisation of an effective
many-body Hamiltonian of a cluster surrounded by an effective field.
This effective Hamiltonian depends on the density matrix $\gamma$.
In this talk we discuss the formulation of the method and its
application to the Hubbard and single-impurity Anderson models
in one and two dimensions. The accuracy of the method is
deponstrated by comparison with the Bethe-Ansatz solution (1D),
density-matrix renormalization group calculations (1D),
and quantum Monte Carlo simulations (2D).