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arXiv:cond-mat/0209673 · International Journal of Modern Physics B

NEW COMPARISONS FOR LOCAL QUANTITIES OF THE TWO-DIMENSIONAL HUBBARD MODEL

Adolfo Avella, Ferdinando Mancini

Published Mar 10, 2003• 2 citations
arXivHTMLPDF

Abstract

We have compared the results of out approximation scheme, the composite operator, method, for the double occupancy and the internal energy of the two-dimensional Hubbard model with numerical data obtained by means of the Lanczos1and quantum Monte Carlo schemes.2The agreement is very good at both half-filling and away from it showing how reliable is the approximation scheme.

DOI
10.1142/s0217979203016224

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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.
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Superconducting correlation of the Hubbard model on a square lattice is reinvestigated by quantum Monte Carlo method. Results from more than one order of magnitude larger Monte Carlo steps than before are presented to discuss the convergence of the data to the ground state. By examining the dependence on the choice of initial trial states as well as on the Trotter number in detail, the superconducting correlation in the ground state is reliably obtained up to 12×12 lattice away from the half-filling and up to 16×16 lattice at the half-filling, which substantially improve former results near the half-filling. Various channels of pairing in the ground state show no system size dependence and remain quite short ranged at any filling including the region close to the half-filling. Numerical data show further evidence that neither extended s - nor d -wave superconducting state is possible in the two-dimensional Hubbard model.