Competition of magnetic and superconducting ordering in one-dimensional generalized Hubbard models

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