We investigate the ground state and the excitation spectrum associated with the localized defect states of the three-quarter-filled, one-dimensional Peierls-Hubbard model. In the continuum limit with an infinite, on-site electron-electron repulsion energy U, the Hamiltonian is mapped onto the N=1 Gross-Neveu model, in which irrationally charged soliton-antisoliton pairs are formed upon doping, while polarons are unstable. Corrections due to finite-U effects are discussed. However, discreteness effects are found to support excitations absent from the continuum field theory. In particular, for large band separation a novel type of polaron can be formed with a highly localized electronic wave function surrounded by an extended pattern of local lattice distortion.
We study the effects of charge degrees of freedom on the spin excitation dynamics in quasi-one-dimensional magnetic materials. Using the density matrix renormalization group method, we calculate the dynamical spin structure factor of the Hubbard model at half electronic filling on a chain and on a ladder geometry, and compare the results with those obtained using the Heisenberg model, where charge degrees of freedom are considered frozen. For both chains and two-leg ladders, we find that the Hubbard model spectrum qualitatively resembles the Heisenberg spectrum---with low-energy peaks resembling spinonic excitations---already at intermediate on-site repulsion as small as $U/t\ensuremath{\sim}2--3$, although ratios of peak intensities at different momenta continue evolving with increasing
U/t converging only slowly to the Heisenberg limit. We discuss the implications of these results for neutron scattering experiments and we propose criteria to establish the values of
U/t of quasi-one-dimensional systems described by one-orbital Hubbard models from experimental information.
We propose an effective model called the ``charge model,'' for the half-filled one-dimensional Hubbard and extended Hubbard models. In this model, spin-charge separation, which has been justified from an infinite on-site repulsion (
U) in the strict sense, is compatible with charge fluctuations. Our analyses based on the many-body Wannier functions succeeded in determining the optical conductivity spectra in large systems. The obtained spectra reproduce the spectra for the original models well even in the intermediate
U region of
U=5--
10T, with
T being the nearest-neighbor electron hopping energy. These results indicate that the spin-charge separation works fairly well in this intermediate
U region against the usual expectation and that the charge model is an effective model that applies to actual quasi-one-dimensional materials classified as strongly correlated electron systems.