We use the correlated-random-field approximation and a conditional coherent-potential approximation to study the ground-state phase diagram of the one-band Hubbard model. Our approach incorporates both spin and electron correlations. It has been found that for certain values of the parameters of the model, in addition to paramagnetic, ferromagnetic, antiferromagnetic, and spin-glass or spin-liquid phases found in our earlier studies, a phase-separated phase is found to be favored for 0.7\ensuremath{\le}n\ensuremath{\le}1.0 and U/B\ensuremath{\ge}2 in good agreement with results obtained in the t-J model using the technique of the 1/N expansion. The present approach also allows one to watch the dependence of the electron density of states on the number of electrons per site and gives a single physical picture for the occurrence of a metal-insulator transition. Implications of these results for the existence of superconducting ground state as well as comparison to other studies will be briefly discussed.
We use the correlated-random-field approximation and a conditional coherent-potential approximation to study the ground-state phase diagram of the one-band Hubbard model. Our approach incorporates both spin and electron correlations. It has been found that for certain values of the parameters of the model, in addition to paramagnetic, ferromagnetic, antiferromagnetic, and spin-glass or spin-liquid phases found in our earlier studies, a phase-separated phase is found to be favored for 0.7\ensuremath{\le}n\ensuremath{\le}1.0 and U/B\ensuremath{\ge}2 in good agreement with results obtained in the t-J model using the technique of the 1/N expansion. The present approach also allows one to watch the dependence of the electron density of states on the number of electrons per site and gives a single physical picture for the occurrence of a metal-insulator transition. Implications of these results for the existence of superconducting ground state as well as comparison to other studies will be briefly discussed.
The authors use an unrestricted self-consistent mean-field approach to the one-dimensional periodic Hubbard model to study its ground-state phase diagram. Their approach allows one to incorporate spin and electron correlations as well as spin and charge fluctuations. The authors find that a homogeneous antiferromagnetic state exists only at half-filling, where the state is also insulating. Off half-filling, it was found that the ground state of the Hubbard model consists of clusters with different magnetic and charge properties. For certain values of the parameters of the system the cluster formation develops to a full phase separation. The effects of the intersite repulsive or attractive interaction on the ground-state properties were also examined. Implications of the authors results for the existence of a superconducting ground state as well as comparison with other studies will be briefly discussed.
Numerical and analytical studies of several models of correlated electrons are discussed. Based on exact diagonalization and variational Monte Carlo techniques, we have found indications that the two-dimensional t-J model superconducts near phase separation in the regime of quarter-filling density, in agreement with previous results reported by Dagotto and Riera [Phys. Rev. Lett. 70, 682 (1993)]. At this density the dominant channel is dx2-y2, but a transiton to s-wave superconductivity is observed decreasing the electronic density. In addition, the one-band t-U-V model has also been studied using a mean-field approximation. An interesting region of dx2-y2 superconductivity near phase separation is observed in the phase diagram, and its implications for recent self-consistent studies of d-wave condensates in the context of the high-Tc cuprates are briefly discussed. Finally, the two-band Hubbard model on a chain is also analyzed. Superconducting correlations near phase separation exist in this model, as it occurs in the t-J model. Based on these nontrivial examples it is conjectured that electronic models tend to have superconducting phases in the vicinity of phase separation, and this regime of parameter space should be explored first when a new model for superconductivity is proposed. Reciprocally, if it is established that a model does not phase separate, even in an extended parameter space, then we believe that its chances of presenting a superconducting phase are considerably reduced.
The description of a solid at a microscopic level is complex, involving the interaction of a huge number of its constituents, such as ions or electrons.The Hubbard model used in this research describes interacting electrons in narrow energy bands, with application to problems as diverse as high -Tc superconductivity, band magnetism and the metal-insulator transition.This research seeks to solve one of the most challenging problems in Theoretical physics which is to describe electronic correlations.In this research the t -U Hubbard model is used to solve analytically and numerically using the exact diagonalization techniques This research work focused on the spin interaction and magnetic behavior of some systems and it is therefore an investigation into the various phenomena seen in the phase diagram of ferromagnetic systems.We studied the 2 electrons on 2 sites, 2 electrons on 3 sites and 2 electrons on 4 sites all in One-Dimension (1-D), where the onsite coulomb repulsion, U, and the hopping matrix element, t, were varies to determine their magnetic phase diagram.This results obtained shows that, as the values of the onsite coulomb repulsion, U, increases in all the lattice systems studied, the electronic correlation that favours ferromagnetism gets stronger, but there were no clear transition, and at some point the lattices loss its antiferromagnetic properties, hence the instability of ferromagnetism were established.It was also observed that as the hopping matrix element, t, increases the electronic correlation that favours ferromagnetism get stronger and the lattice begins to loss antiferromagnetic properties but beyond the transition point the lattice began to gain a much stronger antiferromagnetism, hence the ferromagnetism is unstable.
The description of a solid at a microscopic level is complex, involving the interaction of a huge number of its constituents, such as ions or electrons. The Hubbard model used in this research describes interacting electrons in narrow energy bands, with application to problems as diverse as high – Tc superconductivity, band magnetism and the metal-insulator transition. This research seeks to solve one of the most challenging problems in Theoretical physics which is to describe electronic correlations. In this research the t – U Hubbard model is used to solve analytically and numerically using the exact diagonalization techniquesThis research work focused on the spin interaction and magnetic behavior of some systems and it is therefore an investigation into the various phenomena seen in the phase diagram of ferromagnetic systems. We studied the 2 electrons on 2 sites, 2 electrons on 3 sites and 2 electrons on 4 sites all in One-Dimension (1-D), where the onsite coulomb repulsion, U, and the hopping matrix element, t, were varies to determine their magnetic phase diagram.This results obtained shows that, as the values of the onsite coulomb repulsion, U, increases in all the lattice systems studied, the electronic correlation that favours ferromagnetism gets stronger, but there were no clear transition, and at some point the lattices loss its antiferromagnetic properties, hence the instability of ferromagnetism were established. It was also observed that as the hopping matrix element, t, increases the electronic correlation that favours ferromagnetism get stronger and the lattice begins to loss antiferromagnetic properties but beyond the transition point the lattice began to gain a much stronger antiferromagnetism, hence the ferromagnetism is unstable.
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.
By using variational wave functions and quantum Monte Carlo techniques, we investigate the interplay between electron-electron and electron-phonon interactions in the two-dimensional Hubbard-Holstein model. Here, the ground-state phase diagram is triggered by several energy scales, i.e., the electron hopping t, the on-site electron-electron interaction U, the phonon energy ${\ensuremath{\omega}}_{0}$, and the electron-phonon coupling g. At half filling, the ground state is an antiferromagnetic insulator for $U\ensuremath{\gtrsim}2{g}^{2}/{\ensuremath{\omega}}_{0}$, while it is a charge-density-wave (or bipolaronic) insulator for $U\ensuremath{\lesssim}2{g}^{2}/{\ensuremath{\omega}}_{0}$. In addition to these phases, we find a superconducting phase that intrudes between them. For ${\ensuremath{\omega}}_{0}/t=1$, superconductivity emerges when both U/t and $2{g}^{2}/t{\ensuremath{\omega}}_{0}$ are small; then, by increasing the value of the phonon energy ${\ensuremath{\omega}}_{0}$, it extends along the transition line between antiferromagnetic and charge-density-wave insulators. Away from half filling, phase separation occurs when doping the charge-density-wave insulator, while a uniform (superconducting) ground state is found when doping the superconducting phase. In the analysis of finite-size effects, it is extremely important to average over twisted boundary conditions, especially in the weak-coupling limit and in the doped case.