Quantum Fluctuations due to Spinons, Polarons, and Stripes in the Two-Dimensional Hubbard Model

Quantum fluctuations (QF's) in the two-dimensional Hubbard model are visualized by superposition of optimized nonorthogonal Slater determinants. In the half-filled system, QF's consist of rotational and translational motions of spinon-antispinon pairs, while in the lightly doped systems (delta = 0.96), those motions of polarons form the QF's. It is shown that an attractive interaction works between two polarons, in the framework of a projected Hartree-Fock picture. At about 10% doping, the ground state has a stripe structure and QF's due to deviations from the uniform stripe. The present method gives the ground state energies comparable or in some cases superior to the variational Monte Carlo method with a Gutzwiller projection parameter.