We investigate the ground state properties of the one- and the two-dimensional Hubbard models using a new variational Monte Carlo method. By generalizing the Gutzwiller variational wave function (GF) to take into account an off-diagonal intersite correlation, we examine the metal-insulator transition mechanism at the half filling. As Kaplan et al. first pointed out, the binding mechanism between doubly occupied sites and empty sites plays a crucial role for this transition; we confirm this by examining the real space correlation function between these two kinds of sites. Results for the spin and the charge structure factors are presented as well as the momentum distribution function and are discussed in connection with the pairing effect. We also find that in less-than half filling, the improvements of the structure factors at 2 k F are realized as compared with GF results.
Quantum Monte Carlo methods are used to study a quantum phase transition in a one-dimensional Hubbard model with on-site interaction U and a staggered ionic potential $(\ensuremath{\Delta}).$ Using recently formulated methods, the electronic polarization and localization are determined directly from the correlated ground state wave function and compared to results of previous work using exact diagonalization and Hartree-Fock. We find a transition from a symmetric band insulator to a broken-symmetry bond ordered (BO) phase as the ratio of $U/\ensuremath{\Delta}$ is increased, with a metallic point at the transition. Since it is known that at $\ensuremath{\Delta}=0$ the usual Hubbard model is a Mott insulator (MI) with no long-range order, we have searched for a second transition to this state by (i) increasing U at fixed $\ensuremath{\Delta}$ and (ii) decreasing $\ensuremath{\Delta}$ at fixed U. We find no transition from the BO to MI state, and we propose that the symmetric MI state exists only at $\ensuremath{\Delta}\ensuremath{\equiv}0.$
Phase diagrams of the one-dimensional extended Hubbard model with a nearest neighbor interaction
V and site-off-diagonal (bond-charge
X and bond-bond
W) interactions at half-filling are obtained numerically, using the level-crossing approach for finite-size clusters. This analysis is straightforward extension of the preceding work [cond-mat/9909277], where only the
X term is considered as a site-off-diagonal term. Similarly to the
X term, the
W term enlarges bond-charge-density-wave (BCDW) and bond-spin-density-wave (BSDW) phases for
W<0 and
W>0 cases, respectively. In the strong-coupling region, however, the
W term causes ferromagnetism for
W>0, and shifts the boundary of the phase separation in the
U/t≪−1 region, which are different from the roles of the
X term. In addition, we discuss a parameter region where the BSDW state is the exact ground state, and show that the exactly solvable point appears just on the phase boundary between the BSDW and the ferromagnetic phases.
A one-dimensional model of interacting electrons with on-site U, nearest-neighbor V, and correlated-hopping interaction
T∗ is studied at half filling using the continuum-limit field theory approach. The ground-state phase diagram is obtained for a wide range of coupling constants. In addition to the insulating spin- and charge-density wave phases for large U and V, respectively, we identify bond-located ordered phases corresponding to an enhanced Peierls instability in the system for ${T}^{*}>0, |U\ensuremath{-}2V|<{8T}^{*}/\ensuremath{\pi}$ and to a staggered magnetization located on bonds between sites for ${T}^{*}<0, |U\ensuremath{-}2V|<8|{T}^{*}|/\ensuremath{\pi}.$ The general ground-state phase diagram including insulating, metallic, and superconducting phases is discussed.
We investigate the ground-state phase diagram of the one-dimensional 'ionic' Hubbard model with an alternating periodic potential at half-filling by numerical diagonalization of finite systems with the Lanczos and density matrix renormalization group methods. We identify an insulator–insulator phase transition from a band to a correlated insulator with simultaneous charge and bond-charge order. The transition point is characterized by the vanishing of the optical excitation gap while simultaneously the charge and spin gaps remain finite and equal. Indications for a possible second transition into a Mott-insulator phase are discussed.