General recursive relation for the calculation of the local Green’s function in the resolvent-matrix approach

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Abstract
In this paper we present a general recursive scheme which provides the basis for an efficient calculation of the local Green’s function in the resolvent-matrix approach. To test the validity and the efficiency of the scheme, we applied it to calculate the bulk density of states of a crystalline GaP. Since the eigenstates in a crystalline solid are all extended, this case study should provide a stringent test for the efficiency of the convergence procedure. The result of the case study indicates that the general recursive relation eliminates the redundancy in the calculation of the local Green’s function, thus improving the efficiency of the convergence procedure. Furthermore, the case study also demonstrates that the convergence procedure can yield results as accurately as one desires even under the most unfavorable conditions.