Numerical Approaches to Coupled Quantum Systems

Computational physics has proven to be highly successful in revealing valuable insight into strongly correlated many body systems. The purpose of this lecture is threefold. Firstly, we present ubiquitous model hamiltonians tailored to describe different constituents of strongly correlated many body systems individually. Secondly, a collection of modern numerical techniques, currently employed to study such models, is discussed in great detail to provide insight into the pros and cons of these approaches. Finally, we will apply these numerical approaches to coupled quantum systems ‘the manganites’ and study some of their fascinating features.