1. Solutions of the Two-Dimensional Hubbard Model:Benchmarks and Results from a Wide Range of Numerical Algorithms
- Author
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Ireneusz W. Bulik, Thomas M. Henderson, Federico Becca, Andrew J. Millis, X. Liu, Garnet Kin-Lic Chan, Chia-Min Chung, Carlos A. Jiménez-Hoyos, Igor S. Tupitsyn, Shiwei Zhang, Nikolay Prokof'ev, Bo-Xiao Zheng, Steven R. White, Gustavo E. Scuseria, Zhenyue Zhu, Luca F. Tocchio, Hao Shi, Michel Ferrero, Boris Svistunov, Emanuel Gull, Andrey E. Antipov, Youjin Deng, Mingpu Qin, James P.F. LeBlanc, Evgeny Kozik, Scuola Internazionale Superiore di Studi Avanzati / International School for Advanced Studies (SISSA / ISAS), Centre National de la Recherche Scientifique (CNRS), Centre de Physique Théorique [Palaiseau] (CPHT), Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X), Chaire Physique de la matière condensée (A. Georges), Collège de France (CdF (institution)), University of Washington [Seattle], Department of Chemistry, Rice University [Houston], University of Twente [Netherlands], Departement of clinical neurophysiology, St Bartolomew's Hospital, Department of Physics, College of William and Mary [Williamsburg] (WM), Leblanc, Jpf, Antipov, Ae, Becca, Federico, Bulik, Iw, Chan, Gkl, Chung, Cm, Deng, Yj, Ferrero, Michel, Henderson, Tm, Jimenez Hoyos, Ca, Kozik, E, Liu, Xw, Millis, Aj, Prokof'Ev, Nv, Qin, Mp, Scuseria, Ge, Shi, H, Svistunov, Bv, Tocchio, Luca Fausto, Tupitsyn, I, White, Sr, Zhang, Sw, Zheng, Bx, Zhu, Zy, and Gull, E.
- Subjects
infinite dimensions ,Hubbard model ,QC1-999 ,Quantum Monte Carlo ,diagrammatic monte-carlo ,Monte Carlo method ,Extrapolation ,FOS: Physical sciences ,General Physics and Astronomy ,coupled-cluster method ,electron correlation ,Condensed Matter - Strongly Correlated Electrons ,ground-state ,quantum impurity models ,Statistical physics ,d-wave superconductivity ,heisenberg antiferromagnets ,Physics ,[PHYS]Physics [physics] ,Quantum Physics ,Strongly Correlated Electrons (cond-mat.str-el) ,Density matrix renormalization group ,matrix renormalization-group ,mean-field theory ,Condensed Matter Physics ,Coupled cluster ,Thermodynamic limit ,Diffusion Monte Carlo ,cond-mat.str-el ,Astronomical and Space Sciences - Abstract
International audience; 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 multi-reference projected Hartree-Fock. 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.
- Published
- 2015