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 left angle Sz(i) right angle, its fluctuations left angle Sz(i)2 right angle - left angle Sz(i) right angle 2 and various spin correlation functions left angle Sz(i)Sz(j) right angle - left angle Sz(i) right angle left angle Sz(j) right angle are determined as a function of the Coulomb interaction strength U/t. The local magnetic moments left angle Sz(i) right angle increase monotonically with increasing Coulomb repulsion U/t showing antiferromagnetic order between nearest neighbors [ left angle Sz(0) right angle ≅- left angle Sz(1) right angle ]. At large U/t, left angle Sz(i) right angle is strongly reduced with respect to the saturation value 1/2 due to exchange fluctuations between nearest neighbors (NN) spins [ vertical stroke left angle Sz(i) right angle vertical stroke ≅0.35 for U/t→+∞]. left angle Sz(i)2 right angle - left angle Sz(i) right angle 2 shows a maximum for U/t=2.4-2.9 that results from the interplay between the usual increase of left angle Sz(i)2 right angle with increasing U/t and the formation of important permanent moments left angle Sz(i) right angle at large U/t. While NN sites show antiferromagnetic 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. (orig.)