We study the magnetic properties of the two-dimensional Hubbard model with nearest-neighbor (t) and next-nearest-neighbor (t2) hopping and on-site repulsion U. We first calculate the mean-field phase diagram as a function of band filling and U. Because of the Van Hove singularity in the density of states, we find a ferromagnetic phase extending to zero U for certain band filling. For the half-filled band case, antiferromagnetism sets in at a finite value of U if t»0. We study the behavior of spin-spin correlation functions for small lattices of up to N =64 atoms using MonteCarlo simulations, as well as exact diagonalization for N =4. Our results show enhanced ferromagnetic correlations in some regions, but apparently no ferromagnetic long-range order. In the halffilled case, our numerical results are consistent with a nonzero critical U. For a non-half-filled band our results suggest that there is no long-range order.

We write the Hamiltonian of the Bose gas with two-body repulsive δ-function potential in a pseudoparticle operator basis which diagonalizes the problem via the Bethe ansatz. In this operator basis the original bosonic interactions are represented by zero-momentum forward-scattering interactions between Landau-liquid pseudoparticles. We find that this pseudoparticle operator algebra is complete: all the Hamiltonian eigenstates are generated by acting pseudoparticle operators on the system vacuum. It is shown that one boson of vanishing momentum and energy is a composite of a one-pseudoparticle excitation and a collective pseudoparticle excitation. These excitations have finite opposite momenta and cannot be decomposed.Our formalism enables us to calculate the various quantities which characterize the static and dynamic behavior of the system at low energies.

We study the phase diagram of the one-dimensional extended Hubbard model in the half-filledband sector for an attractive nearest-neighbor interaction V. A first-order condensation transition occurs at a critical value of V which is a function of the on-site repulsion U. We obtain the phase boundary in strong coupling for U~oo and U~-ao, and, from a variational estimate, for U=0.%'e then compute the phase boundary numerically using a Monte Carlo simulation technique. Our numerical estimates join smoothly the strong-coupling regimes for~U~-4, and agree with the variational estimate at U =0 within 10%.

This paper mainly studies the ferromagnetic fluctuations of two types of bilayer triangular lattices on the basis of single-band Hubbard model. First, according to the tight-binding model, energy spectrum, the density of states and spin susceptibility can be obtained analytically. Second, we take finite Coulomb interaction into account, apply the random-phase approximation and do the determinant quantum Monte Carlo simulation. Finally, this paper makes comparisons of magnetic properties of two types of bilayer triangular lattices, and the effects of the interlayer coupling are also discussed in detail.