Variational description of the ground state of the repulsive two-dimensional Hubbard model in terms of nonorthogonal symmetry-projected Slater determinants
Rodríguez-Guzmán, R.; Jiménez-Hoyos, Carlos A.; Scuseria, Gustavo E.
The few-determinant (FED) methodology, introduced in our previous works [R. Rodríguez-Guzmán et al., Phys. Rev. B 87, 235129 (2013); Phys. Rev. B 89, 195109 (2014)] for one-dimensional (1D) lattices, is here adapted for the repulsive two-dimensional Hubbard model at half filling and with finite doping fractions. Within this configuration mixing scheme, a given ground state with well-defined spin and space group quantum numbers is expanded in terms of a nonorthogonal symmetry-projected basis determined through chains of variation-after-projection calculations. The results obtained for the ground-state and correlation energies of half-filled and doped 4×4,6×6,8×8, and 10×10 lattices, as well as momentum distributions and spin-spin correlation functions in small lattices, compare well with those obtained using other state-of-the-art approximations. The structure of the intrinsic determinants resulting from the variational strategy is interpreted in terms of defects that encode information on the basic units of quantum fluctuations in the considered 2D systems. The varying nature of the underlying quantum fluctuations, reflected in a transition to a stripe regime for increasing on-site repulsions, is discussed using the intrinsic determinants belonging to a 16×4 lattice with 56 electrons. Such a transition is further illustrated by computing spin-spin and charge-charge correlation functions with the corresponding multireference FED wave functions. In good agreement with previous studies, the analysis of the pairing correlation functions reveals a weak enhancement of the extended s-wave and dx2−y2 pairing modes. Given the quality of results here reported together with those previously obtained for 1D lattices and the parallelization properties of the FED scheme, we believe that symmetry projection techniques are very well suited for building ground-state wave functions of correlated electronic systems, regardless of their dimensionality.