This school is part of a series that was started with the ''soft matter'' school in 2011, and continued in 2012 with the ''electronic structure'' school and “DNA physics” in 2013. The aim of the school is to make the students familiar with the numerical techniques used in their field of (condensed matter) physics, and to allow them to gain some practice by actually implementing some of these numerical techniques.

Although the school focuses on methodological (algorithmic and computational) issues, each session is centered on a guiding theme in terms of physical applications, so that the lectures can include physical examples of general interest to the audience.

The number and quality of applications received for previous schools, with a very international audience (including strong participations from US and Indian groups) has shown that there is a real need for such introductory schools.

The school has been approved by the scientific board of the Les Houches physics school and the date (23/6-4/7/2014) has already been decided.

The quantitative description of degenerate and strongly correlated quantum many-body systems is the main subject of the 2014 school on computational physics. The courses will introduce the state-of-the-art approaches, e.g. quantum Monte Carlo [1,2], dynamical mean-field [3,4], and density matrix renormalization group methods [5]. These courses will focus on the physics of ultracold atomic gases [6], which is particularly suited for a pedagogical introduction, as experiments directly realize fundamental models of quantum many-body theory and enable quantitative comparisons in correlation-dominated regimes. More recent developments and present trends at the interface with other condensed matter systems will be exposed in short lectures and seminars.

This school will be organized in a relatively short set of long lectures (5 lectures of 4x1h30) supplemented by evening seminars and presentations by participants (5-7x1,5h) and a poster session. The lectures will focus on computational and methodological aspects of the research, and the lecturers will also propose numerical hands-on exercises. Students are invited to practice during the afternoons, with the technical support of engineers from the Blaise Pascal Center of the ENS Lyon.

The lecturers are expected to stay at the physics center for a large part of the duration of the school, so as to maximize the interaction with the students.

Main lectures (together with some speakers who provisionally agreed to contribute) are :

1) Gross-Pitaevskii and classical field theory (Alice Sinatra, ENS, Paris)

2) Quantum Monte Carlo methods in the continuum:

a) Introduction in Monte Carlo methods at zero temperature (Saverio Moroni, SISSA, Trieste),

b) Finite temperature path integral calculations (Lode Pollet, LMU, München)

3) Quantum Monte Carlo calculations on a lattice (Stefan Wessel, RWTH, Aachen)

4) Dynamical mean field theory (Philipp Werner, Fribourg)

5) Density matrix renormalization group (Corinna Kollath, Bonn)

Within the main courses the students should be introduced to the basic methodology illustrated with simple applications in the field of quantum gases. More advances applications will be presented by seminars and overview talks. Potential speakers are M. Davis (1), S. Giorgini (2a), M. Boninsegni (2b), N. Prokof’ev (1-3), D. Ceperley (2/3), A. Georges (4), I. Cirac, U. Schollwöck (5).

Short introductions or overview talks on tensor network algorithms (P. Corboz), high-temperature series expansions, exact diagonalization (D. Poilblanc, Q. Läuchli), and the physics of quantum simulators (interface between experiments and simulations) are further envisaged.