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A multi-reference configuration mixing scheme is used to describe the groundstate, characterized by well defined spin and space group symmetry quantumnumbers as well as doping fractions $N_{e}/N_{sites}$, of one dimensionalHubbard lattices with nearest-neighbor hopping and periodic boundaryconditions. Within this scheme, each ground state is expanded in a given numberof nonorthogonal and variationally determined symmetry-projectedconfigurations. The results obtained for the ground state and correlationenergies of half-filled and doped lattices with 30, 34 and 50 sites, comparewell with the exact Lieb-Wu solutions as well as with the ones obtained withother state-of-the-art approximations. The structure of the intrinsicsymmetry-broken determinants resulting from the variational procedure isinterpreted in terms of solitons whose translational and breathing motions canbe regarded as basic units of quantum fluctuations. It is also shown that inthe case of doped 1D lattices, a part of such fluctuations can also beinterpreted in terms of polarons. In addition to momentum distributions, bothspin-spin and density-density correlation functions are studied as functions ofdoping. The spectral functions and density of states, computed with an ansatzwhose quality can be well-controlled by the number of symmetry-projectedconfigurations used to approximate the $N_{e} \pm 1$ electron systems, displayfeatures beyond a simple quasiparticle distribution, as well as spin-chargeseparation trends.

Multi-reference symmetry-projected variational approximation for the ground state of the doped one-dimensional Hubbard model