We present results of Monte Carlo simulations of the three-dimensional half-filled Hubbard model on simple-cubic
43 lattices and some
63 lattices with periodic boundary conditions, as well as of small clusters embedded in an effective medium. Magnetic properties were studied for values of the Hubbard repulsion U ranging from 0 to the bandwidth W=12t (t is the hopping matrix element). Our results show that antiferromagnetism is enhanced up to U\ensuremath{\sim}(5/6)W and then suppressed. The q=0 magnetic susceptibility is enhanced by U, although much less than predicted by the random-phase approximation. The transition temperature to an antiferromagnetic state is found to have a broad maximum around U\ensuremath{\sim}(5/6)W, with a maximum value of approximately W/18. The implications of our results for superconductivity in the attractive Hubbard model are also discussed.
We develop series expansions for the ground state properties of the Hubbard model by introducing an Ising anisotropy into the Hamiltonian. For the two-dimensional square lattice half-filled Hubbard model, the ground state energy, local moment, sublattice magnetization, uniform magnetic susceptibility, and spin stiffness are calculated as a function of U/t, where U is the Coulomb constant and t is the hopping parameter. Magnetic susceptibility data indicate a crossover around U\ensuremath{\approxeq}4 between spin density wave antiferromagnetism and Heisenberg antiferromagnetism. Comparisons with Monte Carlo simulations, random phase approximation result, and mean-field solutions are also made.
The antiferromagnetic Ne\'el temperature
TN is calculated as a function of the Coulomb interaction U for a half-filled 3D Hubbard model. Numerical results are given for the specific heat and staggered magnetic suspectibility on periodic lattices ranging from
43--
103 sites, and used to determine
TN. The size dependence of the results suggests that the transition is weakly first order at small to intermediate values of U.
We have investigated the antiferromagnetic phase of two-dimensional (2D), three-dimensional (3D), and extended Hubbard models on a bipartite cubic lattice by means of the composite operator method within a two-pole approximation. This approach yields a fully self-consistent treatment of the antiferromagnetic state that respects the symmetry properties of both the model and the algebra. The complete phase diagram, as regards the antiferromagnetic and paramagnetic phases, has been drawn. We first reported, within a pole approximation, three kinds of transitions at half-filling: Mott-Hubbard, Mott-Heisenberg, and Heisenberg transitions. We have also found a metal-insulator transition, driven by doping, within the antiferromagnetic phase. This latter is restricted to a very small region near half-filling, and has, in contrast to what has been found by similar approaches, a finite critical Coulomb interaction as a lower bound at half-filling. Finally, it is worth noting that our antiferromagnetic gap has two independent components: one due to the antiferromagnetic correlations, and another coming from the Mott-Hubbard mechanism.
The cluster slave-spin method is employed to investigate systematically the ground state properties of the Hubbard model on a square lattice with doping $\ensuremath{\delta}$ and coupling strength
U being its parameters. At half-filling, a relation between the staggered magnetization
M and the antiferromagnetic (AFM) gap ${\mathrm{\ensuremath{\Delta}}}_{\text{AFM}}$ is established in the small
U limit to compare with that from the Hartree-Fock theory, and a first-order metal-insulator Mott transition in the paramagnetic state is substantiated, which is characterized by discontinuities and hystereses at
UMott=10t. The interaction
Uc for the crossover in the AFM state, separating the weak- and strong-coupling regimes, is found to remain almost unchanged with large dopings, and smaller than
UMott at half-filling because of long range AFM correlations. Finally, an overall phase diagram in the $U\ensuremath{-}\ensuremath{\delta}$ plane is presented, which is composed of four regimes: the AFM insulator at half-filling, the AFM metal with the compressibility $\ensuremath{\kappa}>0$ or $\ensuremath{\kappa}<0$, and the paramagnetic metal, as well as three phase transitions: (i) From the AFM metal to the paramagnetic metal, (ii) between the AFM metal phases with positive and negative $\ensuremath{\kappa}$, and (iii) separating the AFM insulating phase at $\ensuremath{\delta}=0$ from the AFM metal phase for $\ensuremath{\delta}>0$.
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
E, average local magnetization $ $, its fluctuations $ - ^2$ and various spin correlation functions $ - $ are determined as a function of the Coulomb interaction strength
U/t. The calculated local magnetic moments $ $ increase monotonically with increasing Coulomb repulsion
U/t forming an antiferromagnetic spin-density-wave state which matches the two sublattices of the bipartite Bethe lattice. At large
U/t, $ $ is strongly reduced with respect to the saturation value 1/2 due to exchange fluctuations between nearest neighbors (NN) spins (
∣∣≃0.35 for
U/t→+∞). $ - ^2$ shows a maximum for
U/t=2.4--2.9 which results from the interplay between the usual increase of $ $ with increasing
U/t and the formation of important permanent moments $ $ at large
U/t. NN sites show antiferromagnetic spin correlations which increase with increasing Coulomb repulsion. In contrast next NN sites are very weakly correlated over the whole range of
U/t. The accuracy of the DMRG results is discussed by comparison with tight-binding exact results, independent DMRG calculations for the Heisenberg model and simple first-order perturbation estimates.