Theoretical Solid State Physics

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Summer School on "Computational Methods for Quantum Materials"

26.05.2014  -  06.06.2014

Numerical methods are playing a more and more prominent role in many of the forefront fields of research: Quantum magnetism, Quantum liquids, Bose-Einstein condensates, Quantum Computing, cuprate and pnictide High-Temperature superconductors are a few examples.

This School will focus on computational tools for so-called "quantum materials" whose spectacular properties are consequences of the non-trivial quantum mechanical nature of 14-ecolematter. Examples of spectacular electronic properties arising from quantum mechanics include high-temperature superconductivity and perfect metallic behavior at the surfaces of topological insulators.

The School will illustrate and contribute to the dramatic cross-fertilization that is occurring between ab initio approaches and those developed for highly correlated quantum materials such as Dynamical Mean-Field Theory (DMFT), Continuous-Time Quantum Monte Carlo approaches, Density Matrix Renormalization Group, Quantum Cluster Approaches (Dynamical Cluster Approximation, Cellular Dynamical Mean-Field Theory, Variational Cluster Approximation). We will also discuss ideas from quantum information that have led to dramatic improvements in methods such as the Density Matrix Renormalization Group.

The importance of ab-initio methods with strong spin-orbit scattering has also increased with the recent interest on topological insulators. The merging of ab-initio methods with those for strongly correlated quantum materials now allows one to make ab-initio predictions for materials with d and f electrons that were unimaginable until recently. The serious student of theoretical physics cannot afford to ignore these methods and the physical insights they have brought.

The codes for the most powerful established algorithms are freely accessible on the Web through the ABNIT and ALPS projects in Europe. The main purpose of this Summer School is to give an in-depth introduction to the main numerical methods currently employed in various fields of theoretical many-body physics so that the student will be able to use these methods, become familiar with the breakthroughs they allowed and be able to make a critical appraisal of each method's relative strengths and weaknesses.

Hands-on training on ABINIT and ALPS codes will be an integral part of the School. There will also be hands-on training on a Wien2K+DMFT code and on the new ITensor code for DMRG..

This School will thus help train the next generation of Researcher to use and develop tools that have become crucial to solve important problems that are intractable with standard analytical approaches. Many new avenues of research will be open to them, for example strongly correlated topological insulators, one of the next frontiers. They will also be taught a few "good practice" programming techniques that should be helpful to them in a broad range of job opportunities.

Sherbrooke, Québec, Canada