**Lecture Series on
****Quantum Physics in
One Dimension**

Thierry Giamarchi, University of Geneva

Program:

Lecture 1: Basics of one dimensional systems - basics of electronic interactions in solids; Fermi liquid theory - Basic models of interacting systems (Heisenberg, Hubbard and Bose-Hubbard, Lieb-Lininger) - peculiarities of one dimensional systems - some experimental realizations in condensed matter and cold atomic gases - Glimpse of the various methods to tackle one dimensional systems (Bethe Ansatz, DMRG Bosonization)

Lecture Notes Lecture 2: Bosonization and Luttinger liquid physics - Bosonization of bosons - Luttinger liquid concept - Spin systems - Systems with internal degrees of freedom, bosons, Fermions - fractionalization of excitations, spin-charge separation - Experimental checks Lecture 3: Perturbations on a Luttinger liquid - Periodic lattice: Mott transition (bosons and fermions) - Effect of disorder: Bose Glass and Anderson localization - Coupling between chains: quasi-one dimensional systems and ladders Lecture 4: Beyond Luttinger liquid I would like at the moment to keep this lecture open, since it might depend from the interest of the audience. But as a potential teaser for possible content: - Band curvature effects - Non Luttinger liquids - Luttinger liquids in presence of a bath or of noise - Coupled chains and deconfinement transition