Numerische Methoden für Vielteilchensysteme

Tuesday 14-16, Thursday 9-11, Seminaraum 5.

This course is intended for students from the 5th semester onwards.  It covers a series of modern topics in solid state physics with emphasis placed on numerical methods.  For example, the Hubbard model is the generic model required to understand the physics of transition metal oxides, a class of organic materials, as well as the physics of optical lattices.  Impurity models, such as the Anderson model, are the key to the understanding of  heavy fermion materials,  the Kondo effect in quantum dots, as well as the  physics of transition metal oxides in the limit where the coordination number is very large. Here is   a tentative outline of the course.     

1.      The Monte Carlo Method

a.       The central limit theorem

b.      Generating Markov chains

c.       The one dimensional Ising model. Exact solution and Monte Carlo simulation.

2.      Introduction to models of correlated electron systems

a.       Hubbard model

b.      The Heisenberg model

c.       The Anderson impurity model.

d.      The Kondo model.

3.      Simulations of quantum spin models

a.       Trotter decomposition.

b.      The world line path integral formulation of the Hesenberg model.

c.       Local and loop updates.

d.      Stochastic series expansions.

e.       Aspects of the physics of quantum antiferromagnets.

4.      Auxiliary field methods.

a.       The Hirsch-Fye impurity algorithm.

b.      The Kondo resonance and the Kondo effect in quantum dots.

c.       Application of the Hirsch-Fye algorithm to dynamical mean-field theories .

5.      Exact diagonalization methods. Ground state static and dynamical properties.