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TT: Fachverband Tiefe Temperaturen
TT 9: CE: (General) Theory 1
TT 9.3: Talk
Monday, March 14, 2011, 14:30–14:45, HSZ 201
Numerical correlation-energy functional for lattice density-functional theory: A systematic approach to the ground-state properties of strongly correlated systems — •Matthieu Saubanere and Gustavo Pastor — Institut für Theoretische Physik Heinrich-Plett-Str. 40 D-34132 Kassel
We present an accurate method to determine ground-state properties of strongly-correlated electrons described by lattice-model Hamiltonians. In lattice density-functional theory (LDFT) the basic variable is the one-particle density matrix γ. From the HK theorem, the ground state Energy Egs[γgs] = minγ E[γ] is obtained by minimizing the energy over all the representable γ. The energy functional can be divided into two contributions: the kinetic-energy functional, which linear dependence on γ is exactly known, and the correlation-energy functional W[γ], which approximation constitutes the actual challenge. Within the framework of LDFT, we develop a numerical approach to W[γ], which involves the exact diagonalization of an effective many-body Hamiltonian of a cluster surrounded by an effective field. This effective Hamiltonian depends on the density matrix γ. 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 demonstrated by comparison with the Bethe-Ansatz solution (1D), density-matrix renormalization group calculations (1D), and quantum Monte Carlo simulations (2D).