We present the algorithmic details of the dynamical cluster approximation (DCA), with a quantum Monte Carlo (QMC) method used to solve the effective cluster problem. The DCA is a fully-causal approach which systematically restores nonlocal correlations to the dynamical mean field approximation (DMFA) while preserving the lattice symmetries. The DCA becomes exact for an infinite cluster size, while reducing to the DMFA for a cluster size of unity. We present a generalization of the Hirsch-Fye QMC algorithm for the solution of the embedded cluster problem. We use the two-dimensional Hubbard model to illustrate the performance of the DCA technique. At half-filling, we show that the DCA drives the spurious finite-temperature antiferromagnetic transition found in the DMFA slowly towards zero temperature as the cluster size increases, in conformity with the Mermin-Wagner theorem. Moreover, we find that there is a finite temperature metal to insulator transition which persists into the weakcoupling regime. This suggests that the magnetism of the model is Heisenberg like for all non-zero interactions. Away from half-filling, we find that the sign problem that arises in QMC simulations is significantly less severe in the context of DCA. Hence, we were able to obtain good statistics for small clusters. For these clusters, the DCA results show evidence of non-Fermi liquid behavior and superconductivity near halffilling.

The opening of a critical-fluctuation-induced pseudogap ͑or precursor pseudogap͒ in the one-particle spectral weight of the half-filled two-dimensional Hubbard model is discussed. This pseudogap, appearing in our Monte Carlo simulations, may be obtained from many-body techniques that use Green functions and vertex corrections that are at the same level of approximation. Self-consistent theories of the Eliashberg type ͑such as the fluctuation exchange approximation͒ use renormalized Green functions and bare vertices in a context where there is no Migdal theorem. They do not find the pseudogap, in quantitative and qualitative disagreement with simulations, suggesting these methods are inadequate for this problem. Differences between precursor pseudogaps and strong-coupling pseudogaps are also discussed.

We present well-controlled results on the metal to insulator transition (MIT) within the paramagnetic solution of the dynamical cluster approximation (DCA) in the two-dimensional Hubbard model at half-filling. In the strong coupling regime, a local picture describes the properties of the model; there is a large charge gap ∆ ≈ U . In the weak-coupling regime, we find a symbiosis of short-range antiferromagnetic correlations and moment formation cause a gap to open at finite temperature as in one dimension. Hence, this excludes the mechanism of the MIT proposed by Slater long ago.Introduction In this letter we report the study of the metal-insulator transition (MIT) and its relation to antiferromagnetism (AFM) in the two-dimensional (2D) Hubbard model at half-filling. Results from numerical simulations [1,2] have convincingly shown that the ground state of the model is an AF insulator, with the Néel temperature constrained to be T N = 0 by the Mermin-Wagner theorem. However, the nature of the MIT is less clear, as there are two conflicting opinions concerning the MIT and its relation to AFM. The first opinion [3][4][5] is that the strong and weak coupling MI transitions are very different. When the local Coulomb repulsion parameter U is larger than the non-interacting band width W , the ground state is an insulator with a large charge gap ∆ ≈ U . The MIT occurs well before the onset of magnetism at the temperature T g ≈ U , and the spin and charge degrees of freedom are decoupled. The superexchange interaction couples the spins with the exchange constant |J| ≈ 4t 2 /U , and the spins govern the low-energy physics. This type of MIT, which is purely due to local correlations, is called a Mott transition. In weak coupling, a spin density wave (SDW) instability develops at T = 0 because of the nesting of the Fermi surface. The MIT is the direct consequence of the Brillouin zone folding generated by magnetic ordering. This type of MIT will be referred to as a Slater transition. It is believed that this regime can be well described by the usual many-body weak-coupling approaches. The second opinion, is due to Anderson [6] who has argued that the strong-coupling behavior presented above occurs for both strong and weak coupling so that a Mott gap is present for all U > 0 as in one dimension. As the temperature falls, local moments develop first because of the MIT and then they order so that AFM is the consequence of the MIT, not the converse. Because of this strong interaction, there is no adiabatic continuity between the

We study the pseudogaps in the spectra of the 2D Hubbard model using both finite-size and dynamical cluster approximation (DCA) quantum Monte Carlo calculations. At half-filling, a charge pseudogap, accompanied by non-Fermi-liquid behavior in the self-energy, is shown to persist in the thermodynamic limit. The DCA (finite-size) method systematically underestimates (overestimates) the width of the pseudogap. A spin pseudogap is not seen at half-filling. At finite doping, a divergent d-wave pair susceptibility is observed.