  Quantum cluster theories are a set of approaches for the theory of correlated
and disordered lattice systems, which treat correlations within the cluster
explicitly, and correlations at longer length scales either perturbatively or
within a mean-field approximation. These methods become exact when the cluster
size diverges, and most recover the corresponding (dynamical) mean-field
approximation when the cluster size becomes one. Here we will review systematic
dynamical cluster simulations of the two-dimensional Hubbard model, that
display phenomena remarkably similar to those found in the cuprates, including
antiferromagnetism, superconductivity and pseudogap behavior. We will then
discuss results for the structure of the pairing mechanism in this model,
obtained from a combination of dynamical cluster results and diagrammatic
techniques.
