Density-matrix renormalization study of the Hubbard model [4]on a Bethe lattice

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 <Ŝ_z(i)>, its fluctuations <Ŝ_z(i)²> — <Ŝ_z(i)²> and various spin correlation functions <Ŝ_z(i)Ŝ_z(j)> — <Ŝ_z(i)><S_z(j)> are determined as a function of the Coulomb interaction strength U/t. The local magnetic moments <Ŝ_z(i)> increase monotonically with increasing Coulomb repulsion U/t showing antiferromagnetic order between nearest neighbors [〈Ŝ_z(0)〉≃ ̶ 〈Ŝ_z(1)〉]. At large U/t, <Ŝ_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)〉|≃ 0.35 for U/t→+∞]. <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 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.