Multireference symmetry-projected variational approaches for ground and excited states of the one-dimensional Hubbard model
Abstract
We present a multireference configuration mixing scheme for describing ground and excited states, with well-defined spin and space-group symmetry quantum numbers, of the one-dimensional Hubbard model with nearest-neighbor hopping and periodic boundary conditions. Within this scheme, each state is expanded in terms of nonorthogonal and variationally determined symmetry-projected configurations. The results for lattices up to 30 and 50 sites compare well with the exact Lieb-Wu solutions as well as with results from other state-of-the-art approximations. In addition to spin-spin correlation functions in real space and magnetic structure factors, we present results for spectral functions and density of states computed with an Ansatz whose quality can be well controlled by the number of symmetry-projected configurations used to approximate the systems with $$N_e$$ and $$N_e±1$$ electrons. The intrinsic symmetry-broken determinants resulting from the variational calculations have rich structures in terms of defects that can be regarded as basic units of quantum fluctuations. Given the quality of the results here reported, as well as the parallelization properties of the considered scheme, we believe that symmetry-projection techniques, which have found ample applications in nuclear structure physics, deserve further attention in the study of low-dimensional correlated many-electron systems.
- Authors:
-
- Rice Univ., Houston, TX (United States). Dept. of Chemistry, and Dept. of Physics and Astronomy
- Rice Univ., Houston, TX (United States). Dept. of Chemistry
- Publication Date:
- Research Org.:
- Rice Univ., Houston, TX (United States); Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States). Oak Ridge Leadership Computing Facility (OLCF)
- Sponsoring Org.:
- USDOE Office of Science (SC)
- OSTI Identifier:
- 1565048
- Alternate Identifier(s):
- OSTI ID: 1103865
- Grant/Contract Number:
- SC0001474
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Physical Review. B, Condensed Matter and Materials Physics
- Additional Journal Information:
- Journal Volume: 87; Journal Issue: 23; 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., Schutski, R., and Scuseria, Gustavo E. Multireference symmetry-projected variational approaches for ground and excited states of the one-dimensional Hubbard model. United States: N. p., 2013.
Web. doi:10.1103/physrevb.87.235129.
Rodríguez-Guzmán, R., Jiménez-Hoyos, Carlos A., Schutski, R., & Scuseria, Gustavo E. Multireference symmetry-projected variational approaches for ground and excited states of the one-dimensional Hubbard model. United States. https://doi.org/10.1103/physrevb.87.235129
Rodríguez-Guzmán, R., Jiménez-Hoyos, Carlos A., Schutski, R., and Scuseria, Gustavo E. Sat .
"Multireference symmetry-projected variational approaches for ground and excited states of the one-dimensional Hubbard model". United States. https://doi.org/10.1103/physrevb.87.235129. https://www.osti.gov/servlets/purl/1565048.
@article{osti_1565048,
title = {Multireference symmetry-projected variational approaches for ground and excited states of the one-dimensional Hubbard model},
author = {Rodríguez-Guzmán, R. and Jiménez-Hoyos, Carlos A. and Schutski, R. and Scuseria, Gustavo E.},
abstractNote = {We present a multireference configuration mixing scheme for describing ground and excited states, with well-defined spin and space-group symmetry quantum numbers, of the one-dimensional Hubbard model with nearest-neighbor hopping and periodic boundary conditions. Within this scheme, each state is expanded in terms of nonorthogonal and variationally determined symmetry-projected configurations. The results for lattices up to 30 and 50 sites compare well with the exact Lieb-Wu solutions as well as with results from other state-of-the-art approximations. In addition to spin-spin correlation functions in real space and magnetic structure factors, we present results for spectral functions and density of states computed with an Ansatz whose quality can be well controlled by the number of symmetry-projected configurations used to approximate the systems with $N_e$ and $N_e±1$ electrons. The intrinsic symmetry-broken determinants resulting from the variational calculations have rich structures in terms of defects that can be regarded as basic units of quantum fluctuations. Given the quality of the results here reported, as well as the parallelization properties of the considered scheme, we believe that symmetry-projection techniques, which have found ample applications in nuclear structure physics, deserve further attention in the study of low-dimensional correlated many-electron systems.},
doi = {10.1103/physrevb.87.235129},
journal = {Physical Review. B, Condensed Matter and Materials Physics},
number = 23,
volume = 87,
place = {United States},
year = {Sat Jun 01 00:00:00 EDT 2013},
month = {Sat Jun 01 00:00:00 EDT 2013}
}
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