In the present work the numerical density matrix renormalization group (DMRG) algorithm is used to analyze the ground state properties of the Hubbard model with transverse spin-exchange. The DMRG algorithm, which was developed by White in 1992, is based on the following simple but effective concept: the ground-state wavefunction as well as the low energy excitations of a large interacting chain are obtained by increasing the lattice size iteratively, starting with a small one that can be diagonalized exactly. The exponentially growing Hilbert space is controlled by a renormalization procedure in which 'less important' degrees of freedom are integrated out. Motivated by recent experimental findings showing evidence for the competition or even coexistence of triplet superconductivity and ferromagnetism we focused our investigations on a rather simple extension of the Hubbard model including transverse spin exchange between electrons on nearest-neighbour sites. In the half-filled case, we showed that the phase diagram obtained in the weak-coupling limit has to be modified. A new phase, described by spin and charge excitation gap, shows long-range order in the longitudinal spin correlation, whereas superconducting correlations are surpressed and decay exponentially as expected for the case of a finite charge gap. In general, the presence of a repulsive on-site Coulomb interaction U leads to an enlargement of the sectors with nonvanishing charge gap at the expense of the sectors with spin gap. We extend our analysis to the case of a quarter-filled band. Depending on the value J/t the model belongs either to a gapless excitation phase or to a spin gapped phase with gapless charge degrees of freedom.
In this paper we study the ground-state phase diagram of a one-dimensional $t\ensuremath{-}U\ensuremath{-}J$ model, at half-filling. In the large-bandwidth limit and for ferromagnetic exchange with easy-plane anisotropy, a phase with gapless charge and massive spin excitations, characterized by the coexistence of triplet superconducting and spin density wave instabilities is realized in the ground state. With reduction of the bandwidth, a transition into an insulating phase showing properties of the spin-
21 XY model takes place. In the case of weakly anisotropic antiferromagnetic exchange the system shows a long-range dimerized (Peierls) ordering in the ground state. The complete weak-coupling phase diagram of the model, including effects of the on-site Hubbard interaction, is obtained.
We calculate spin and charge excitation spectra of the one-dimensional (1D) quarter-filled Hubbard model with nearest-neighbor
t and next-nearest-neighbor ${t}^{\ensuremath{'}}$ hopping integrals using the dynamical density-matrix renormalization group technique. We consider a case where
t (>0) is much smaller than ${t}^{\ensuremath{'}}$
(>0). First, we examine the accuracy of our method based on comparison between our result and exact noninteracting spectrum. Next, we investigate the spectra with the on-site Coulomb interaction. We find that the spin and charge excitation spectra are essentially the same as those of the 1D quarter-filled Hubbard (and $t\text{\ensuremath{-}}J$) model for the two 1D chains along the hopping integral ${t}^{\ensuremath{'}}$. However, the hopping integral
t $(<{t}^{\ensuremath{'}})$ plays a crucial role in the short-range correlations and low-energy excitaions; ferromagnetic correlation between electrons on neighboring sites is enhanced and pairing correlation between the electrons is induced. Consequently, a spin-triplet superconducting state may be derived.
We study the phase diagram of a one-dimensional extended Hubbard model with antiferromagnetic exchange interaction analytically and numerically. The bosonization and transfer-matrix renormalization group methods are used in the corresponding coupling regimes. At half-filling, the system is a Mott insulator with a finite spin excitation gap if the on-site Coulomb repulsion is fairly smaller than the antiferromagnetic exchange
J. This Mott insulator is characterized by the bond-charge-density-wave order or spontaneously dimerization. In the weak-coupling regime where the spin-charge separation holds approximately, the critical point separating the gapless and gapped spin liquid phases is ${U}_{c}\ensuremath{\sim}J∕2$. However, as
J increases, the spin-charge couplings become important and the critical point
Uc is significantly suppressed and eventually tends to zero as $J\ensuremath{\rightarrow}\ensuremath{\infty}$. Away from half-filling, the charge gap completely collapses but the spin gap persists.
We study the ground-state properties of the double-chain Hubbard model coupled with ferromagnetic exchange interaction by using the weak-coupling theory, density-matrix renormalization-group technique, and Lanczos exact-diagonalization method. We determine the ground-state phase diagram in the parameter space of the ferromagnetic exchange interaction and band filling. We find that, in high electron-density regime, the spin gap opens and the spin-singlet
dxy-wave-like pairing correlation is most dominant, whereas in low electron-density regime, the fully-polarized ferromagnetic state is stabilized where the spin-triplet
py-wave-like pairing correlation is most dominant.
We studied ferromagnetism in the one-dimensional Hubbard model with doubly degenerate atomic orbitals by means of the density-matrix renormalization-group method and obtained the ground-state phase diagrams. It was found that ferromagnetism is stable from low to high
(0<n<1.75) electron density when the interactions are sufficiently strong. The quasi-long-range order of triplet superconductivity coexists with the ferromagnetic order for a strong Hund coupling region, where the interorbital interaction ${U}^{\ensuremath{'}}\ensuremath{-}J$ is attractive. At quarter-filling
(n=1), the insulating ferromagnetic state appears, accompanying orbital quasi-long-range order. For low densities
(n<1), ferromagnetism occurs owing to the ferromagnetic exchange interaction caused by virtual hoppings of electrons, the same as in the quarter-filled system. This comes from separation of the charge and spin-orbital degrees of freedom in the strong-coupling limit. This ferromagnetism is fragile against variation of band structure. For high densities
(n>1), the phase diagram of the ferromagnetic phase is similar to that obtained in infinite dimensions. In this case, the double exchange mechanism is operative for stabilizing the ferromagnetic order and this long-range order is robust against variation of the band dispersion. A partially polarized state appears in the density region $1.68\ensuremath{\lesssim}n\ensuremath{\lesssim}1.75$ and phase separation occurs for n just below the half-filling
(n=2).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.