Automated analytic solutions to many-electron problems

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Despite the dizzying array of existing high-energy subatomic particles that have been discovered, in our day-to-day lives we interact with only four: neutrons, protons, electrons and photons (light). These four particles make up all elements on the periodic table and comprise everything you know and love in your life. Electrons, and how they interact with the other three, are the central object of interest in my research program. Electrons are the objects that form current in metals, semi-conductors and insulators. Modern day electronic devices are possible due to our ability to understand and control how electrons move in materials (comprised of neutrons and protons), or react when exposed to light (photons) or an applied voltage. Surprisingly, our understanding of precisely how electrons behave in materials is very rudimentary. The reason for this is that the interactions between electrons scale exponentially with the number of particles, which is on the order of Avogadro's constant (6.02x10^23), making exact calculations intractable.  This is known as the many-electron problem. The key idea is that we cannot overcome this hurdle by simply building bigger or faster computers, but instead require innovative and novel approaches to estimate solutions with less computational expenditure. The goals of this research program are to:I) Develop novel tools for studying the many-electron problem;II) Apply those tools to model systems; III) Extend those tools to study materials.  To accomplish these goals we will employ a method recently developed in our group that allow us to instantaneously solve a dominant fraction of correlated electron problems, a key advantage over other methods. Our tools will be applied to model systems in order to test and improve our numerical algorithms. To begin, we will study the Hubbard model, which is the quintessential model of correlated electron systems. Over the course of this program, we will extend beyond the restrictions of that model to allow more general interactions of interest to quantum chemistry. This will allow us to take incremental steps from purely theoretical model systems, towards real material calculations. As an additional component of the program we intend to develop well-tested software codes that can solve correlated electron systems with the intent of releasing these codes as open-source tools. This will allow other research groups to optimally benefit from our efforts. The proposed work will contribute significantly to the detailed understanding of interacting systems.  A full understanding of the interplay between spin and charge degrees of freedom in quantum systems will allow for the intelligent design of materials and will therefore be of impact to both fundamental research programs and drive forward technological advancement to the benefit of industry, the economy, and Canada.