M. Potthoff et W. Nolting, THE LARGE-U HUBBARD-MODEL FOR A SEMIINFINITE CRYSTAL - A MOMENT APPROACH AND AN ENERGY-DEPENDENT RECURSION METHOD, Journal of physics. Condensed matter, 8(27), 1996, pp. 4937-4958
Electron-correlation effects at metal surfaces can be studied qualitat
ively within the framework of the Hubbard model for a semi-infinite la
ttice. We propose a moment approach for an approximate determination o
f the local electronic self-energy that is applicable for systems with
reduced translational symmetry. For the strong-correlation regime a o
ne-pole ansatz for the self-energy can be motivated. All a priori unkn
own parameters in the ansatz for the self-energy are calculated self-c
onsistently by exploiting the equality between two alternative but exa
ct representations for the first four moments of the spectral density.
With the resulting expression for the self-energy at hand, the many-b
ody problem reduces to the problem of finding the local density of sta
tes (LDOS) for an energy-dependent effective one-particle Hamiltonian.
We determine the LDOS for the semi-infinite system using a straightfo
rward generalization of the standard tight-binding recursion method th
at is suitable for treating an energy-dependent Hamiltonian. The resul
ting energy dependence of the recursion coefficients is studied in det
ail for the (100) surface of a bcc crystal and an interpolation proced
ure for a numerically feasible evaluation of the theory is suggested.