Incremental expansions for the ground state energy of the two-dimensional Hubbard model

A generalization of Faddeev’s approach of the 3-body problem to the many-body problem leads to the method of increments. This method was recently applied to account for the ground state properties of Hubbard-Peierls chains (JETP Letters 67 (1998) 1052). Here we generalize this approach to two-dimensional square lattices and explicitely treat the incremental expansion up to third order. Comparing our numerical results with various other approaches (Monte Carlo, cumulant approaches) we show that incremental expansions are very efficient because good accuracy with those approaches is achieved treating lattice segments composed of 8 sites only.