DESCRIPTION of MEETING
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 matter. 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.
About two-thirds of the schooling time will be spent learning numerical methods, but each one will also be abundantly illustrated with applications on topics of current research interest.
Formal presentations will be in the morning and just before a late dinner. There will thus be posters sessions and ample time for discussions in the afternoon.
We will begin the School with an experimental introduction that will motivate the rest of the lectures.
This is a summer school so students are at the center of this event. The 2008 and 2012 summer schools were highly appreciated in part because of the effort to coordinate speakers and topics such that they could be presented in a pedagogical manner. We intend to continue this tradition. There will be two poster sessions where students can present their work. Questions are encouraged and hands-on sessions give ample time for students to interact with Faculty and with each other.
Students should have at least one year of graduate work and be familiar with advanced quantum mechanics and statistical mechanics. A few places will be available to Postdocs and Faculty members. Exceptionally, they can request to attend only part of the school. International students need to obtain a visa or to show their admission letter upon entry, depending on their country of origin.
All students can register for this School as a three credit PhD level course with Universite de Sherbrooke (there will be 45 hours of lecture, equivalent to a one-semester course). There are no fees for registration or tuition to the course. There will be a discount on living expenses for those that register for credit.