705760 Selected topics in strongly correlated systems

winter semester 2013/2014 | Last update: 28.03.2014 Place course on memo list
705760
Selected topics in strongly correlated systems
SV 1
2
Block
annually
English

At the end of the course, the student should be familiar with some basics concepts in the theory of strongly correlated systems, such as symmetries and symmetry breaking, duality transformations, gauge symmetry and topological matter. In addition, the student should be able to identify the key driving mechanism for phase transitions in low-dimensional systems.


Ising and XX models:

-brief review of phenomenology and symmetry, mean field solution;

-fermionization: the Jordan-Wigner transformation;

-Bogoliubov decoupling.

Ising model in two-dimensions:

- duality with Ising Lattige gauge theories: Hilbert space, Hamiltonian and Wilson Loops;

- gauge invariance in classical statistical mechanics: a note on the 8-vertex model;

- phase diagram of Ising lattice gauge theories.

Basic topological matter:

- braiding statistics: beyond fermions and bosons;

- the Kitaev chain: exact solution and phase diagram;

- Majorana fermions as non-Abelian anyons.

An additional topic on strongly correlated systems will also be covered along the course. The specific topic will be discussed with the students after the first lecture; possible suggestions include:

- introduction to one-dimensional systems: low-energy approaches;

- introduction to Ice-models;

- basics of electronic systems: the Hubbard model;

- exact solution of the Lieb-Liniger model and connections with ultra-cold gases.

Continuous assessment (based on regular written and/or oral contribution by participants).

Course examination according to § 7, statute section on "study-law regulations"

Will be discussed in the first lesson.

Quantum mechanics; statistical mechanics (basics); a background in group theory, quantum field theory and quantum many-body theory is suggested, although not fundamental.

18.12.2013
Wed, Dec. 18, 10:00-12:00, Besprechungsraum, IQOQI
Thu, Dec. 19, 10:00-12:00, Erwin-Schrödinger-Saal, IQOQI
Tue, Jan. 7, 10:00-12:00, Erwin-Schrödinger-Saal, IQOQI
Thu, Jan. 9, 10:00-12:00, Erwin-Schrödinger-Saal, IQOQI
Mon, Jan. 13, 14:00-16:00, Besprechungsraum, IQOQI
Tue, Jan. 14, 10:00-12:00, Erwin-Schrödinger-Saal, IQOQI