COMPARISON OF CALCULATIONS FOR THE HUBBARD-MODEL OBTAINED WITH QUANTUM-MONTE-CARLO, EXACT, AND STOCHASTIC DIAGONALIZATION

In this paper we compare numerical results for the ground state of the Hubbard model obtained by Quantum-Monte-Carlo simulations with result s from exact and stochastic diagonalizations. We find good agreement f or the ground state energy and superconducting correlations for both, the repulsive and attractive Hubbard model. Special emphasis lies on t he superconducting correlations in the repulsive Hubbard model, where the small magnitude of the values obtained by Monte-Carlo simulations gives rise to the question, whether these results might be caused by f luctuations or systematic errors of the method. Although are notice th at the Quantum-Monte-Carlo method has convergence problems for large i nteractions, coinciding with a minus sign problem, we confirm the resu lts of the diagonalization techniques for small and moderate interacti on strengths. Additionally we investigate the numerical stability and the convergence of the Quantum-Monte-Carlo method in the attractive ca se, to study the influence of the minus sign problem on convergence. A lso here in the absence of a minus sign problem we encounter convergen ce problems for strong interactions.