  A multi-reference configuration mixing scheme is used to describe the ground
state, characterized by well defined spin and space group symmetry quantum
numbers as well as doping fractions $N_{e}/N_{sites}$, of one dimensional
Hubbard lattices with nearest-neighbor hopping and periodic boundary
conditions. Within this scheme, each ground state is expanded in a given number
of nonorthogonal and variationally determined symmetry-projected
configurations. The results obtained for the ground state and correlation
energies of half-filled and doped lattices with 30, 34 and 50 sites, compare
well with the exact Lieb-Wu solutions as well as with the ones obtained with
other state-of-the-art approximations. The structure of the intrinsic
symmetry-broken determinants resulting from the variational procedure is
interpreted in terms of solitons whose translational and breathing motions can
be regarded as basic units of quantum fluctuations. It is also shown that in
the case of doped 1D lattices, a part of such fluctuations can also be
interpreted in terms of polarons. In addition to momentum distributions, both
spin-spin and density-density correlation functions are studied as functions of
doping. The spectral functions and density of states, computed with an ansatz
whose quality can be well-controlled by the number of symmetry-projected
configurations used to approximate the $N_{e} \pm 1$ electron systems, display
features beyond a simple quasiparticle distribution, as well as spin-charge
separation trends.
