Magnetic and charge correlations in the frustrated 2D Hubbard model

The high temperature superconductors have motivated numerous theoretical studies of strongly correlated many-body systems for over two decades. The richness of the phase diagram of these materials belies their relatively simple quasi-two-dimensional structure of stacked CuO$_2$ planes, where copper ions form a square lattice. With the experimental observation of several complex phases, including superconductivity, in quasi-two-dimensional triangular lattice materials (e.g., Na$_x$CoO$_2$ $\cdot y$H$_2$O and $\kappa$-(ET)$_2$X) we now have material systems in which geometric frustration plays a prominent role. With this as our motivation, we investigate the 2D Hubbard model on a series of lattice geometries. We report preliminary results from mean-field calculations of the charge and magnetic properties of our model on frustrated and non-frustrated lattices. We also discuss the potential application of the constrained path quantum Monte Carlo (CPQMC) method to the study of frustrated 2D Fermi systems.