Quantum Monte Carlo Simulations of the Hubbard Model

The Hubbard model is a model for electrons on a lattice where the only interaction between electrons is an on-site Coulomb interaction. Compared to any physical system it is vastly simplified, but the Hubbard model is believed to be sufficiently complex to explain the important properties of a variety of physical systems, including high-temperature superconductors. The behavior of the Hubbard model depends crucially on the density of electrons in the system. We will discuss enhancements to the current quantum Monte Carlo methods that allow the extraction of information about different fillings of electrons within a single Monte Carlo simulation. This greatly improves the efficiency of studies of the quantum systems that require results from a range of fillings. Unfortunately, simulations of the Hubbard model are limited by a numerical "sign problem" at interesting fillings of electrons.