Computational Quantum Materials
Conceptual advances, new algorithms and the power of modern computers have allowed numerical methods to rank amongst new theoretical frameworks that are indispensable for understanding collective electronic properties of complex solids.
This School will focus on computational tools for both models and ab-initio methods that deal with so-called "quantum materials" whose spectacular properties, ranging from large thermopower, high-temperature superconductors to heavy fermions, topological insulators and colossal magnetoresistance materials, are consequences of the non-trivial quantum mechanical nature of electrons and of their interactions.
The merging of methods for models of strongly correlated quantum materials with ab-initio methods now allows one to make predictions for materials with d and f electrons that were unimaginable until recently. A good part of the School will be devoted to these.
Extensive hands-on training on freely available codes, ABINIT, TRIQS, ITensor and a few others such as LDA+DMFT will be an integral part of the School.
Lectures will be pedagogical, presented in a logical sequence and some review material will make sure students are on the same page.
The School will
- give an in-depth introduction to the main numerical methods used in the study of quantum materials, so that the student will be able to use them, become familiar with the breakthroughs they allowed and be able to make a critical appraisal of each method's relative strengths and weaknesses.
- illustrate and contribute to the dramatic cross-fertilization that is occurring between ab initio Density Functional approaches and methods developed for highly correlated quantum materials such as Dynamical Mean-Field Theory (DMFT), Continuous-Time Quantum Monte Carlo solvers, Density Matrix Renormalization Group, Quantum Cluster Approaches (Dynamical Cluster Approximation, Cellular Dynamical Mean-Field Theory, Variational Cluster Approximation).
- discuss ideas from quantum information that have led to dramatic improvements in methods such as the Density Matrix Renormalization Group.
This School will thus help train the next generation of researchers 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.
Is a package whose main program allows one to find the total energy, charge density and electronic structure of systems made of electrons and nuclei (molecules and periodic solids) within Density Functional Theory (DFT), using pseudopotentials and a planewave or wavelet basis.
TRIQS: A Toolbox for Research on Interacting Quantum Systems
It is an open-source, computational physics library providing a framework for the quick development of applications in the field of many-body quantum physics, and in particular, strongly-correlated electronic systems. It supplies components to develop codes in a modern, concise and efficient way:
A Wien2k-based LDA+DMFT code written by Kristjan Haule for realistic materials calculations
ITensor-Intelligent Tensor-is a C++ library for implementing tensor product wavefunction calculations. It is efficient and flexible enough to be used for research-grade simulations.
A complete DMRG code
Efficient matrix product state class
Quantum number conserving (block-sparse) tensors
Complex numbers (handled lazily: no efficiency loss if real)
This is a summer school so students are at the center of this event. There will be two poster sessions where students can present their work. Questions are encouraged, free time 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.