Welcome to the new version of CaltechAUTHORS. Login is currently restricted to library staff. If you notice any issues, please email coda@library.caltech.edu
Published October 2015 | Published + Accepted Version + Supplemental Material
Journal Article Open

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


Numerical results for ground-state and excited-state properties (energies, double occupancies, and Matsubara-axis self-energies) of the single-orbital Hubbard model on a two-dimensional square lattice are presented, in order to provide an assessment of our ability to compute accurate results in the thermodynamic limit. Many methods are employed, including auxiliary-field quantum Monte Carlo, bare and bold-line diagrammatic Monte Carlo, method of dual fermions, density matrix embedding theory, density matrix renormalization group, dynamical cluster approximation, diffusion Monte Carlo within a fixed-node approximation, unrestricted coupled cluster theory, and multireference projected Hartree-Fock methods. Comparison of results obtained by different methods allows for the identification of uncertainties and systematic errors. The importance of extrapolation to converged thermodynamic-limit values is emphasized. Cases where agreement between different methods is obtained establish benchmark results that may be useful in the validation of new approaches and the improvement of existing methods.

Additional Information

Published by the American Physical Society under the terms of the Creative Commons Attribution 3.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. Received 9 May 2015; revised manuscript received 30 October 2015; published 14 December 2015. We acknowledge the Simons Foundation for funding. The work at Rice University was supported by Grant No. NSF-CHE-1462434. G. K. C. acknowledges funding from the U.S. Department of Energy (DOE) for the development of the DMET method through Grant No. DE-SC0010530, and for its application to the Hubbard model and superconductivity through Grant No. DE-SC0008624. F. B. and L. F. T. acknowledge support from PRIN 2010_2010LLKJBX. S. Z. and H. S. acknowledge support from the National Science Foundation Grant No. DMR-1409510 for AFQMC method development. M. Q. was also supported by DOE Grant No. DE-SC0008627, and A. E. A. by DOE Grant No. ER 46932. Y. D. and X.W. L. acknowledge support from NSFC Grant No. 11275185. The AFQMC calculations were carried out at the Oak Ridge Leadership Computing Facility at the Oak Ridge National Laboratory, and at the computational facilities at the College of William and Mary.

Attached Files

Published - PhysRevX.5.041041.pdf

Accepted Version - 1505.02290.pdf

Supplemental Material - Data_supplemental.zip


Files (32.3 MB)
Name Size Download all
1.3 MB Preview Download
1.2 MB Preview Download
29.8 MB Preview Download

Additional details

August 22, 2023
October 24, 2023