Cluster approximation for an infinite-dimensional determinant

A systematic approximation scheme is proposed for the evaluation of the determinant of an infinite-dimensional matrix which is encountered with, for example, in the theoretical study of Fermion aggregate. This scheme is compatible with the cluster variation method for Ising problems since the combination of the two methods ensures that the total probability is unity. It is useful for the extension of the Gutzwiller variation method in the electron correlation problem.