Quantum Monte Carlo and semiclassical methods are used to solve two- and four-site cluster dynamical mean-field approximations to the square-lattice Hubbard model at half filling and strong coupling. The dyanmical cluster approximation, cluster dynamical mean-field theory, and fictive-impurity approaches are compared. The energy, spin correlation function, phase boundary, and electron spectral function are computed and compared to available exact results. The comparision permits a quantitative assessment of the ability of the different methods to capture the effects of intersite spin correlations. Two real-space methods and one momentum-space representation are investigated. One of the two real-space methods is found to be significantly worse: in it, convergence to the correct results is found to be slow and, for the spectral function, nonuniform in frequency, with unphysical midgap states appearing. Analytical arguments are presented showing that the discrepancy arises because the method does not respect the pole structure of the self-energy of the insulator. Of the other two methods, the momentum-space representation is found to provide the better approximation to the intersite terms in the energy but neither approximation is particularly acccurate and the convergence of the momentum-space method is not uniform. A few remarks on numerical methods are made.

• Received 11 December 2006

DOI:https://doi.org/10.1103/PhysRevB.75.205118