The power of quantum mechanics as a description of nature has never been clearer. But it remains a formidable challenge to solve the equations that are necessary to understand collective electronic properties of complex solids. Conceptual advances, new algorithms and the power of modern computers have allowed numerical methods to rank amongst new theoretical frameworks that are indispensable for this purpose.
This School will focus on computational tools for both models and ab-initio methods that deal with so-called «quantum materials» whose spectacular properties range from high-temperature superconductors to large thermopower materials. These properties 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.
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
- introduce the background in many-body theory necessary to understand modern computational methods. That includes second quantization, Green functions, functional integrals and functional derivative methods, RPA, GW and TPSC approximations.
- 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 in many-body theory for highly correlated quantum materials such as Dynamical Mean-Field Theory (DMFT) and Continuous-Time Quantum Monte Carlo solvers. the steps involved in defining model Hamiltonians from Density Functional approaches will be explained.
- introduce the students to a few current research problems, such as quantum systems out of equilibrium, spin-orbit interactions and topology in electronic structure and to some of the new approaches such as diagrammatic quantum Monte Carlo and materials informatics..
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. 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
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.
Comsuite combines a selection of powerful numerical tools that permit a user to perform first principles calculations for weakly and strongly correlated materials – using extension and simplified versions of dynamical mean-field theory (DMFT) in combination with realistic electronic structure methods.
Wannier90 is an open-source code (released under GPLv2) for generating maximally-localized Wannier functions and using them to compute advanced electronic properties of materials with high efficiency and accuracy.
Z2Pack is a tool for calculating topological invariants. The method is based on tracking the evolution of hybrid Wannier functions, which is equivalent to the computation of the Wilson loop. Originally developed for calculating Z2 invariants, it is now also capable of calculating Chern numbers. Moreover, through the use of individual Chern numbers it can be used to identify any kind of topological phase.
NESSI (Non-Equilibrium Systems Simulation Package)
Is a library that allows one to easily implement calculations with non-equilibrium Green’s functions.
This is a summer school so students are at the center of this event. There will be two official poster sessions where students can present their work, but posters will be exhibited during the whole school to encourage in-depth discussion. 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 Université 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.
|Côté, Michel||Université de Montréal||Introduction to DFT and ABINIT|
|Tremblay, André-Marie||Université de Sherbrooke||Introduction to Many-Body|
|Zingl, Manuel||Flatiron Institute||Wannier and TRIQS|
|Wentzell, Nils||Flatiron Institute||TRIQS|
|Ferrero, Michel||École Polytechnique Paris||Introduction to Monte Carlo, Continuous-Time Quantum Monte Carlo and TRIQS|
|Parcollet, Olivier||Flatiron Institute||TRIQS and Diagrammatic Monte Carlo|
|Georges, Antoine||Flatiron Institute||Dynamical Mean-Field Theory|
|Guo, Hong||McGill||Materials Informatics|
|Kotliar, Gabi||Rutgers University||Realistic Materials Calculations|
|Nourafkan, Reza||Université de Sherbrooke||Introduction to Correlated Materials|
|Gingras, Olivier||Université de Montréal||ABINIT|
|Kutepov, A.L.||Brookhaven National Laboratory||COMSCOPE|
|Choi, Sangcook||Brookhaven National Laboratory||COMSCOPE|
|Haule, Kristjan||Rutgers University||Diagrammatic Monte Carlo|
|Werner, Philipp||Université de Fribourg||NESSI, Non-Equilibrium DMFT|
|Yazyev, Oleg||EPFL Fribourg||Spin-orbit interactions, topology and electronic structure|