** **## Chaines de Spins, Fermions de Dirac, et Systemes Desordonnes

**Bocquet M.** (

*CEA, DSM, SPhT (Service de Physique Théorique), F-91191 Gif-sur-Yvette, FRANCE*)

**Abstract:**

The first part is dedicated to quantum spin chains. We first study
quantum spin systems that are continuously connected to the Heisenberg
spin chain s=1. We build a non-linear sigma model to estimate the spin
gap of those systems. Next we study a s=1/2 spin chain doped by
non-magnetic impurities but which nevertheless possess a nuclear spin.
We use abelian bosonization to calculate the longitudinal relaxation
rate of an impurity and its dependence in the temperature. Logarithmic
corrections to its behavior are also given. We perform the same analysis
on a chiral Luttinger liquid, such as a quantum lead cut in half.
The second part deals with disordered systems in low dimension. We shed
light upon formal links between disordered systems on a network, random
Dirac fermions, non-compact superspin chain and non-linear sigma model.
Details are given on the example of the plateau transition in the
integer quantum Hall effect. Then we perform exact calculations of the
densities of states and typical localization lengths of a Dirac fermion
in 1 dimension in various types of disorder. Many condensed matter
systems are equivalent to this model, such as the random XX quantum
spin chain. Next we study random Dirac fermions in 2 dimensions.
Specifically, we are concerned with the problem of Dirac fermions with
random mass. This model describes low energy excitations of a disordered
$d$-wave superconductor, which impurities are magnetic. A phase diagram
is proposed. It is built around the tricritical point of free Dirac
fermions and shows an unexpected metallic phase for thermal conduction.

**Année de publication ** : 2000

**Thèse ****Soutenance de thèse ** :

* Ecole polytechnique, Palaiseau, France * ; 2000-01-14

**Keywords ** : Quantum spin chains. Inhomogeneous spin chains. Non-linear sigma model. Bosonization. Relaxation rate. Disordered systems. Quantum Hall effect. Dirac fermions High $T_c$ superconductivity

**Langue ** : Français

**Editeurs ** : Jolicoeur T.

** Fichier(s) à télécharger : ** tel-00001560.pdf