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 for 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 charge-charge correlation functions with the corresponding multireference FED wave functions. In good agreement with previous studies, the analysis of themore »
- Authors:
-
- Rice Univ., Houston, TX (United States). Dept. of Chemistry; Rice Univ., Houston, TX (United States). Dept. of Physics and Astronomy
- Rice Univ., Houston, TX (United States). Dept. of Chemistry
- Rice Univ., Houston, TX (United States). Dept. of Chemistry; Rice Univ., Houston, TX (United States). Dept. of Physics and Astronomy
- Publication Date:
- Research Org.:
- Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States). Oak Ridge Leadership Computing Facility (OLCF); Univ. of California, Oakland, CA (United States); Rice Univ., Houston, TX (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC), Basic Energy Sciences (BES)
- OSTI Identifier:
- 1565362
- Alternate Identifier(s):
- OSTI ID: 1179903
- Grant/Contract Number:
- AC02-05CH11231; SC0001474; FG02-09ER16053
- Resource Type:
- Journal Article: Accepted Manuscript
- Journal Name:
- Physical Review. B, Condensed Matter and Materials Physics
- Additional Journal Information:
- Journal Volume: 90; Journal Issue: 19; Journal ID: ISSN 1098-0121
- Publisher:
- American Physical Society (APS)
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; Materials Science; Physics
Citation Formats
Rodríguez-Guzmán, R., Jiménez-Hoyos, Carlos A., and Scuseria, Gustavo E. Variational description of the ground state of the repulsive two-dimensional Hubbard model in terms of nonorthogonal symmetry-projected Slater determinants. United States: N. p., 2014.
Web. doi:10.1103/PhysRevB.90.195110.
Rodríguez-Guzmán, R., Jiménez-Hoyos, Carlos A., & Scuseria, Gustavo E. Variational description of the ground state of the repulsive two-dimensional Hubbard model in terms of nonorthogonal symmetry-projected Slater determinants. United States. https://doi.org/10.1103/PhysRevB.90.195110
Rodríguez-Guzmán, R., Jiménez-Hoyos, Carlos A., and Scuseria, Gustavo E. 2014.
"Variational description of the ground state of the repulsive two-dimensional Hubbard model in terms of nonorthogonal symmetry-projected Slater determinants". United States. https://doi.org/10.1103/PhysRevB.90.195110. https://www.osti.gov/servlets/purl/1565362.
@article{osti_1565362,
title = {Variational description of the ground state of the repulsive two-dimensional Hubbard model in terms of nonorthogonal symmetry-projected Slater determinants},
author = {Rodríguez-Guzmán, R. and Jiménez-Hoyos, Carlos A. and Scuseria, Gustavo E.},
abstractNote = {The few determinant (FED) methodology, introduced in our previous works for 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 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 $d_x2-_y2$ pairing modes. Finally, 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.},
doi = {10.1103/PhysRevB.90.195110},
url = {https://www.osti.gov/biblio/1565362},
journal = {Physical Review. B, Condensed Matter and Materials Physics},
issn = {1098-0121},
number = 19,
volume = 90,
place = {United States},
year = {Fri Nov 07 00:00:00 EST 2014},
month = {Fri Nov 07 00:00:00 EST 2014}
}
Web of Science
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