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Habilitation à diriger des recherches

Dimères classiques en interaction & Autres problèmes en magnétisme quantique

Abstract : This habilitation thesis presents my research activity since about 10 years in quantum magnetism and statistical physics. A particular and pedagogical emphasis is given on the study of a class of statistical mechanics models : interacting dimer models. The first part of this thesis (four chapters) is dedicated to 2d models. After an introduction to dimer coverings in two dimensions, a model of interacting dimers on the square lattice is introduced. Its phase diagram is then studied using numerical simulations (Monte Carlo and transfer matrix) as well as field theory (Coulomb gas): a high-temperature critical phase is separated from an ordered phase by a Kosterlitz-Thouless transition. Several extensions of the original model and their analysis are also presented. The second part (four chapters) deals with the same family of models in three dimensions. The physics is richer, with the occurence of a Coulomb phase and of an unconventional phase transition which de es the standard Ginzburg-Landau theory. A field theory is proposed for the critical point, relating this problem to another class of quantum phase transi- tions, the so-called deconfined quantum critical points. The final shorter part (two chapters) summarizes other research activities in quantum magnetism. We discuss there the quantitative study of magnets in low dimension (in relation with experiments), valence bond physics, deconfined quantum critical points and contributions to the relation between quantum information and condensed matter theories. A short description of future research projects closes this thesis.
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Habilitation à diriger des recherches
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Contributor : Fabien Alet <>
Submitted on : Tuesday, July 31, 2018 - 9:28:55 AM
Last modification on : Thursday, February 27, 2020 - 4:40:05 PM


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  • HAL Id : tel-01798214, version 3


Fabien Alet. Dimères classiques en interaction & Autres problèmes en magnétisme quantique. Mécanique statistique [cond-mat.stat-mech]. Université Paul Sabatier (Toulouse 3), 2016. ⟨tel-01798214v3⟩



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