Eur. Phys. J. B 13, 421-427 (2000)
https://doi.org/10.1007/s100510050053

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

Laboratoire de Physique Quantique (UMR 5626 du CNRS) , IRSAMC, 118 route de Narbonne, 31062 Toulouse Cedex 4, France

Received: 8 February 1999
Revised: 14 June 1999
Published online: 15 February 2000

Abstract

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 , its fluctuations and various spin correlation functions are determined as a function of the Coulomb interaction strength U/t. The local magnetic moments increase monotonically with increasing Coulomb repulsion U/t showing antiferromagnetic order between nearest neighbors []. At large U/t, is strongly reduced with respect to the saturation value 1/2 due to exchange fluctuations between nearest neighbors (NN) spins [ for ]. shows a maximum for U/t=2.4-2.9 that results from the interplay between the usual increase of with increasing U/t and the formation of important permanent moments 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.