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

LeBlanc, J. P. F. and Antipov, Andrey E. and Becca, Federico and Bulik, Ireneusz W. and Chan, Garnet Kin-Lic and Chung, Chia-Min and Deng, Youjin and Ferrero, Michel and Henderson, Thomas M. and Jiménez-Hoyos, Carlos A. and Kozik, E. and Liu, Xuan-Wen and Millis, Andrew J. and Prokof’ev, N. V. and Qin, Mingpu and Scuseria, Gustavo E. and Shi, Hao and Svistunov, B. V. and Tocchio, Luca F. and Tupitsyn, I. S. and White, Steven R. and Zhang, Shiwei and Zheng, Bo-Xiao and Zhu, Zhenyue and Gull, Emanuel (2015) Solutions of the Two-Dimensional Hubbard Model: Benchmarks and Results from a Wide Range of Numerical Algorithms. Physical Review X, 5 (4). Art. No. 041041. ISSN 2160-3308.

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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.

Item Type:Article
Related URLs:
URLURL TypeDescription Material Paper
Antipov, Andrey E.0000-0002-4987-7183
Chan, Garnet Kin-Lic0000-0001-8009-6038
Ferrero, Michel0000-0003-1882-2881
Scuseria, Gustavo E.0000-0002-4635-8126
White, Steven R.0000-0002-0831-9097
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.
Funding AgencyGrant Number
Simons FoundationUNSPECIFIED
Department of Energy (DOE)DE-SC0010530
Department of Energy (DOE)DE-SC0008624
Department of Energy (DOE)DE-SC0008627
Department of Energy (DOE)ER 46932
National Natural Science Foundation of China11275185
Subject Keywords:Computational Physics; Condensed Matter Physics; Strongly Correlated Materials
Issue or Number:4
Record Number:CaltechAUTHORS:20161222-074102137
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:73122
Deposited By: Donna Wrublewski
Deposited On:22 Dec 2016 19:34
Last Modified:09 Mar 2020 13:19

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