Algèbre, intégrabilité et modèles exactement solubles - Département de Physique de l'Ecole Normale supérieure

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Algèbre, intégrabilité et modèles exactement solubles

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Next student seminar :
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Here you can find information about your internships:
Experimental Internship - Undergraduate program
Master ICFP first year Internship

News : ICFP Research seminars
November 14 - 18, 2022 :
All information about the program

Contact us - Student support and Graduate School office :
Tél : 01 44 32 35 60
enseignement@phys.ens.fr

Quick links

Next student seminar :
Access to the program

Here you can find information about your internships:
Experimental Internship - Undergraduate program
Master ICFP first year Internship

News : ICFP Research seminars
November 14 - 18, 2022 :
All information about the program

Contact us - Student support and Graduate School office :
Tél : 01 44 32 35 60
enseignement@phys.ens.fr

Enseignant : Jesper Jacobsen (ENS)
Chargé de TD : Yacine Ikhlef (CNRS)
ECTS : 3
Langue d’enseignement : Anglais
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Description

This course is an introduction to exactly solvable two-dimensional models, considered either in 2D statistical physics, or equivalently as 1D quantum spin chains. Several techniques of resolution will be presented (combinatorics, integrability, conformal invariance, representation theory) with the algebraic content as leitmotif.

Combinatorial methods and free fermions : dimer coverings and the Ising model.

Integrability : Yang-Baxter relation, commuting transfer matrices, coordinate and algebraic Bethe Ansatz.

Lattice algebras : Temperley-Lieb algebra and its representations (6-vertex model, RSOS model, loop model, supersymmetric spin chains), algebraic decomposition of the partition function, Markov trace and Jones-Wenzl projectors.

Conformal field theory : local conformal invariance, Virasoro algebra and its representations, minimal models, modular invariance, Coulomb gas, Liouville field theory.

If time allows, more specialised subjets will also be covered, such as : the Temperley-Lieb algebra with boundaries, supersymmetry, indecomposability at roots of unity, and logarithmic conformal field theories.

Quick links

Next student seminar :
Access to the program

Here you can find information about your internships:
Experimental Internship - Undergraduate program
Master ICFP first year Internship

News : ICFP Research seminars
November 14 - 18, 2022 :
All information about the program

Contact us - Student support and Graduate School office :
Tél : 01 44 32 35 60
enseignement@phys.ens.fr