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