Variational description of the ground state of the repulsive two-dimensional Hubbard model in terms of nonorthogonal symmetry-projected Slater determinants

Abstract

The few determinant (FED) methodology, introduced in our previous works [Phys. Rev. B 87, 235129 (2013) and 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 onsite 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 chargecharge 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 d x 2 −y 2 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.

Solutions of the Two-Dimensional Hubbard Model: Benchmarks and Results from a Wide Range of Numerical Algorithms

“…The calculations presented could in principle be improved in a number of ways: additional symmetries could be broken and restored (such asŜ z or particle number) in the reference configurations; more configurations could be included; and/or a full optimization of all determinants could be performed, in the spirit of the resonating Hartree-Fock approach. 75 The accuracy of any one result can therefore be increased, as shown by Rodríguez-Guzmán et al 76 or by Mizusaki and Imada 77 in the closely related path integral renormalization group (PIRG) approach. Recently, Tahara and Imada 78 have combined the symmetry-projected determinant expansion with short-and long-range Jastrow factors within a variational Monte Carlo framework, which may be used to further increase the accuracy.…”

Communication: Projected Hartree Fock theory as a polynomial similarity transformation theory of single excitations

“…Here, we see that for small on-site repulsion U where the system is weakly correlated, CCD is exceptionally accurate, but that it breaks down completely for larger U; 14,15 SUHF, meanwhile, is reasonable but imperfect everywhere. 16,17 In an ideal world, one could simply combine PHF and coupled cluster, but this task is complicated by the very different natures of the two theories. The PHF wave function is concisely written as a (short) expansion in a set of nonorthogonal broken-symmetry determinants, while the coupled cluster wave function is written as a (long) expansion in a set of orthogonal symmetry-adapted determinants.…”

Required number of states increases only moderately with the problem size for antisymmetrized geminal powers

“…Recently, new results have been reported that are aided by large computing facilities. [25][26][27] These report highly accurate results with the consideration of the spin and spatial symmetry for the Hubbard model as well as qualitatively good results for the selected molecular systems.…”