45th IFF Spring School
Computing Solids: Models, Ab-initio Methods and Supercomputing
10 -21 March 2014 in Jülich, Germany
Computational materials physics is concerned with the complex interplay of the myriad electrons and atoms in a solid, thereby producing a continuous stream of new and unexpected phenomena and forms of matter. An extreme range of length, time, energy and entropy scales gives rise to the complexity of an extremely broad range of solids and associated properties.
There are literally hundreds of thousands of solids. Some solids exhibit useful or exotic phases, such as ferroelectricity, magnetism, superconductivity, or take on exotic states of matter such as the heavy fermion state. Other solids exhibit interesting metal to insulator transitions or show transversal, quantum and non-equilibrium transport processes, to mention but a few.
Every day, new solids are synthesised or grown and novel properties are discovered. These solids find applications as present and emergent materials with specially-designed functionalities on which technological advances in fields such as information technology, energy harvesting, storage and conversion, material science, chemistry and even biology depend.
It sounds rather miraculous, but the formation and stability of all solids and their properties are encoded in the statistical physics and quantum theory of the many electrons in the solid interacting via the Coulomb potential. Therefore, the Schrödinger equation of many electrons provides a fundamental theoretical concept for the understanding of a large variety of quantum phenomena that could be exploited in future technological devices.
The exact solution for this type of Schrödinger equation in a solid is not yet in sight. Instead, over the past decades, powerful theoretical concepts have been developed that allow effective approximations, aimed at reducing complexity while retaining those ingredients necessary for a reliable description of the physical effects in the system.
The approximations of the quantum many-body problem may be roughly divided into three different classes: wave function based methods, ab-initio density functional approaches, and realistic model Hamiltonians, that are solved in part with sophisticated and highly specialized many-body methods such as renormalization techniques or quantum Monte Carlo.
Due to the length and the time scales of the systems investigated, the complexity of the interactions and the possible degree of non-equilibrium, this field has benefited tremendously from the exponential growth of computer resources, in part with new computer architectures. Adapting existing computer codes or developing new codes for these new infrastructures is an increasingly pressing and demanding issue in computational based research.