By means of decimation techniques as applied in the renormalization-group method, a new method is proposed to obtain the effective interactions for two-dimensional Hamiltonians at surfaces. The method has been applied to a simplified model of a transition metal and to Si. For the transition metal we recover well-known results as regards the general properties of the surface density of states, while for Si our results show that an effective two-dimensional Hamiltonian can be introduced along the line proposed by several authors, but with energy-dependent parameters.

• Received 25 January 1983

DOI:https://doi.org/10.1103/PhysRevB.28.4397