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.

Extensive hands-on training on freely available codes, ABINIT__,__ TRIQS__,__ and a few others such as LDA+DMFT and CDMFTS MatDeLab 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

- 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.
- 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), Continuous-Time Quantum Monte Carlo solvers, Quantum Cluster Approaches (Dynamical Cluster Approximation, Cellular Dynamical Mean-Field Theory, Variational Cluster Approximation).
- introduce the students to a few current research problems, such as
*quantum systems out of equilibrium and entanglement in many-body physics*.

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. The school will teach 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.

ABNIT

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:

DFT+Emebedded DMFT Functional:

A Wien2k-based LDA+DMFT code written by Kristjan Haule for realistic materials calculations

Cdmfts-MatDeLab Center for Computational Design of Functional Strongly Correlated Materials and Theoretical Spectroscopy

Is an open source suite of codes, supported by the DOE, MSC program, designed to facilitate material design and theoretical spectroscopy of strongly correlated electron systems.

It geared to go from the crystallographic files that describe the atomic positions, broadly used by material scientists, to the correlation functions measured by experimentalists. It includes a robust electronic platform in an LAPW basis set which can carry out both LDA and quasi-particle self-consistent GW, and multiple many body techniques such as DMFT(dynamical mean field theory) and RISB ( rotationally invariant slave bosons). The user can choose various tradeoffs of speed vs accuracy and treat static and dynamic correlations.

**STUDENT PARTICIPATION **

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.

Please contact organizers for additional information.

The organizers:

André-Marie Tremblay

Michel Côté

Gabi Kotliar

Olivier Parcollet

David Sénéchal