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Single- and multi-band Hubbard models have been found to describe many of thecomplex phenomena that are observed in the cuprate and iron-basedhigh-temperature superconductors. Simulations of these models therefore providean ideal framework to study and understand the superconducting properties ofthese systems and the mechanisms responsible for them. Here we review recentdynamic cluster quantum Monte Carlo simulations of these models, which providean unbiased view of the leading correlations in the system. In particular, wediscuss what these simulations tell us about superconductivity in thehomogeneous 2D single-orbital Hubbard model, and how charge stripes affect thisbehavior. We then describe recent simulations of a bilayer Hubbard model, whichprovides a simple model to study the type and nature of pairing in systems withmultiple Fermi surfaces such as the iron-based superconductors.

Superconductivity in striped and multi-Fermi-surface Hubbard models: From the cuprates to the pnictides