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

Abstract

Numerical results for ground state and excited state properties (energies,\ndouble occupancies, and Matsubara-axis self energies) of the single-orbital\nHubbard model on a two-dimensional square lattice are presented, in order to\nprovide an assessment of our ability to compute accurate results in the\nthermodynamic limit. Many methods are employed, including auxiliary field\nquantum Monte Carlo, bare and bold-line diagrammatic Monte Carlo, method of\ndual fermions, density matrix embedding theory, density matrix renormalization\ngroup, dynamical cluster approximation, diffusion Monte Carlo within a fixed\nnode approximation, unrestricted coupled cluster theory, and multi-reference\nprojected Hartree-Fock. Comparison of results obtained by different methods\nallows for the identification of uncertainties and systematic errors. The\nimportance of extrapolation to converged thermodynamic limit values is\nemphasized. Cases where agreement between different methods is obtained\nestablish benchmark results that may be useful in the validation of new\napproaches and the improvement of existing methods.\n