Numerical simulation of the physical spin and charge response of correlated materials

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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, or react when exposed to light or an applied voltage. Surprisingly, our understanding of precisely how electrons behave in materials is very rudimentary. The root cause of this problem is that the complex interactions between electrons scale exponentially with the number of electrons, which is on the order of Avogadro's constant (6.02x1023). This means that we cannot overcome this many electron problem by simply building bigger or faster computers, but instead require innovative and novel approaches to estimate solutions with less computational expenditure. *** My research program over the next five years will be centered around the development of new numerical procedures to tackle this many-body problem for strongly correlated electron systems; systems that exhibit both metallic and insulating behaviour. (I) We will use statistical methods, known as Quantum Monte Carlo which avoid exponential scaling with system complexity. These methods 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 non-local interactions. This will allow us to take incremental steps from purely theoretical model systems, towards real material calculations. ***(II) As a secondary component of the program, as we develop well tested software codes for handling correlated electron systems, these will be used to solve problems on the short term. This work will be focused on understanding the roles of spin and charge degrees of freedom in the cuprate superconductors, a long standing and open problem in the field of high temperature superconductivity.*** The detailed understanding of interacting systems, and the interplay between spin and charge degrees of freedom will allow for the intelligent design of materials and will therefore be of impact to both fundamental research programs and promote technological development in industry.