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Numerical results for ground state and excited state properties (energies,double occupancies, and Matsubara-axis self energies) of the single-orbitalHubbard model on a two-dimensional square lattice are presented, in order toprovide an assessment of our ability to compute accurate results in thethermodynamic limit. Many methods are employed, including auxiliary fieldquantum Monte Carlo, bare and bold-line diagrammatic Monte Carlo, method ofdual fermions, density matrix embedding theory, density matrix renormalizationgroup, dynamical cluster approximation, diffusion Monte Carlo within a fixednode approximation, unrestricted coupled cluster theory, and multi-referenceprojected Hartree-Fock. Comparison of results obtained by different methodsallows for the identification of uncertainties and systematic errors. Theimportance of extrapolation to converged thermodynamic limit values isemphasized. Cases where agreement between different methods is obtainedestablish benchmark results that may be useful in the validation of newapproaches and the improvement of existing methods.

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