Density-matrix renormalization study of the Hubbard model on a Bethe lattice

The half-filled Hubbard model on the Bethe lattice with coordination number z = 3 is studied using the density-matrix renormalization group (DMRG) method. Ground-state properties such as the energy per site E, average local magnetization ((S) over cap(z)(i)), its fluctuations ((S) over cap(z)(i)(2)) - (S) over cap(z)(i))(2) and various spin correlation functions ((S) over cap(z)(i)(S) over cap(z)(j)) - (S-z(i)) (S-z(j)) are determined as a function of the Coulomb interaction strength U/t. The local magnetic moments (S,(i)) increase monotonically with increasing Coulomb repulsion Tilt showing antiferromagnetic order between nearest neighbors [((S) over cap(z)(0)) similar or equal to - ((S) over cap(z)(1))]. At large U/t, ((S) over cap(z)(i)) is strongly reduced with respect to the saturation value 1/2 due to exchange fluctuations between nearest neighbors (NN) spins [\(S-z(i))\ similar or equal to 0.35 for U/t --> +infinity]. (S-z(i)(2)) - (S-z(i))(2) shows a maximum for U/t = 2.4-2.9 that results from the interplay between the usual increase of (S-z(i)(2)) with increasing U/t and the formation of important permanent:moments (S-z(i)) at large U/t. While NN sites show antiferrornagnetic spin correlations that increase with increasing Coulomb repulsion, the next NN sites are very weakly correlated over the whole range of U/t. The DMRG results are discussed and compared with tight-binding calculations for U = 0, independent DMRG studies for the Heisenberg model and simple first-order perturbation estimates.