Condensed Matter Theory - Département de Physique de l'Ecole Normale supérieure

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Condensed Matter Theory

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Actualités : Séminaire de Recherche ICFP
du 14 au 18 novembre 2022 :
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Contact - Secrétariat de l’enseignement :
Tél : 01 44 32 35 60
enseignement@phys.ens.fr

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Prochain Séminaire de la FIP :
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Retrouvez toutes les informations pour vos stages :
Stages L3
Stages M1 ICFP

Actualités : Séminaire de Recherche ICFP
du 14 au 18 novembre 2022 :
Retrouvez le programme complet

Contact - Secrétariat de l’enseignement :
Tél : 01 44 32 35 60
enseignement@phys.ens.fr

Parcours Matière Condensée / Physique Quantique = COURS OBLIGATOIRE

Enseignant : B.Douçot (UPMC)

Chargé de TD :

Nombre d’ECTS : 6

Langue d’enseignement : Anglais

Description :

The main goal of this course is to cover various examples where strong interactions strongly modify the low energy spectrum of electronic systems, even in absence of any spontaneous symmetry breaking mechanism. We shall therefore focus on strongly interacting electronic liquids.
As an introduction, we will begin to discuss the standard paradigm of Fermi liquids, with an emphasis on response functions and electronic spectral functions. Motivated by the example of high temperature superconductivity in cuprates, we will then address some features of strongly correlated electronic systems such as the Mott transition. The main challenge raised by these systems is that Fermi liquid theory no longer provides a good description of normal state properties, in particular in the pseudogap regime of cuprate superconductors.
We will review some of the theoretical tools, which have been developed to tackle such questions. Another route to witness strong departures from the Fermi liquid paradigm is to consider the case of one-dimensional systems, in which quantum fluctuations are so strong that they deeply modify the nature of electronic quasi-particles. Another striking consequence is the phenomenon of spin and charge separation. We will then discuss the Kondo problem, where a localized spin gets totally screened by a sea of conduction electrons. Besides its intrinsic interest for magnetic alloys, the Kondo problem is still at the heart of many active research themes, such as decoherence of quantum bits induced by their coupling to a macroscopic environment, or quantum transport through nano-systems.
Finally, we will present a brief introduction on quantum Hall effects, which manifest rather striking phenomena, such as a robust quantization of a response function (the Hall conductance), or the emergence of fractional charges and exotic quantum statistics, which interpolate between fermions and bosons.

We plan to have classroom exercises one week out of two.
Topics

1) Nearly free fermionic systems (3 weeks)
Analysis of particle-hole susceptibility : Friedel oscillations around impurities, RKKY interaction. Screening of Coulomb interaction, plasma modes and Landau damping. Moment formation in solids and Stoner instability as examples of the mean-field method.
Single particle properties : calculation of the electronic self-energy for various types of interactions : electron-phonon coupling and electronic interactions. Quasi-particle concept. Connection between electronic spectral function and photo-emission spectra.

2) Mott transitions (2 weeks)
Overview on high temperature superconductors.
Mott insulator in the atomic limit : upper and lower Mott bands. Super exchange interaction in the Mott insulator phase.
Slave rotor picture of the Mott transition.
Sketch of the Dynamical Mean Field Theory method.

3) Luttinger liquids (3 weeks)
Bosonization method for electronic systems in one dimension.
The Luttinger liquid concept.
Spin-charge separation.

4) Kondo problem (3 weeks)
Anderson’s orthogonality catastrophe as an emblematic instance of infra-red divergences in perturbation theory. Illustration on the x-ray edge problem.
Perturbative renormalization group analysis.
Description of the strong coupling fixed point : Nozières’ concept of local Fermi liquid. Numerical non-perturbative implementation of the renormalization group (Wilson). Conformal field-theory picture (Affleck-Ludwig).

5) Introduction to quantum Hall effects (2 weeks)
Physics in a strong magnetic field : projection on the lower Landau levels. Integer effect : quantization of a response function.
Fractional effect : fractional charges and quantum statistics.
Chiral edge-states.

Useful lectures for the Condensed Matter Theory Course :

1) Concepts in solids - P.W Anderson (Addison Wesley)
2) Methods of quantum field theory in statistical physics - A. Abrikosov, L. Gorkov, I. Dzyaloshinskii (Dover)
3) The theory of quantum liquids - D. Pines, P. Nozieres.

Accès rapides

Prochain Séminaire de la FIP :
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Retrouvez toutes les informations pour vos stages :
Stages L3
Stages M1 ICFP

Actualités : Séminaire de Recherche ICFP
du 14 au 18 novembre 2022 :
Retrouvez le programme complet

Contact - Secrétariat de l’enseignement :
Tél : 01 44 32 35 60
enseignement@phys.ens.fr