Structure of the Hilbert-space of the infinite-dimensional Hubbard model

An iterative procedure for the explicit construction of the nontrivial subspace of all symmetry-adapted configurations with non-zero weight in the ground-state of the infinity -dimensional Hubbard model is developed on the basis of a symmetrized representation of the transition operators on a sequence of Bethe-Lattices of finite depth. The relationship between these operators and the well-known mapping of the infinity -dimensional Hubbard model onto an effective impurity problem coupled to a (self-consistent) bath on non-interacting electrons is given. As an application we calculate the properties of various Hubbard stars and give estimates for the half-filled Hubbard model with up to 0.1% accuracy.