Course Summary

This intensive week is intended to provide both a working understanding and real hands-on experience with the essential numerical techniques of solid state many-body physics.
Rather than a 'black-box' philosophy, the course aims to discuss the theory and physics underpinning numerical approaches. Lectures will introduce models of central importance, such as the Ising model, the Anderson impurity model, the Hubbard model and the Heisenberg model. Using these as concrete examples, the Monte Carlo, Exact Diagonalization, Numerical Renormalization Group and Density Matrix Renormalization Group techniques will be discussed. Students will also gain supervised practical hands-on experience writing, using and modifying simple computer codes to solve real problems.

Date, time, location

5--9th March 2012
09:30--17:00 daily
Institute of Theoretical Physics, Cologne

Suited for

Masters and PhD students
Basic experience in computer programming (eg. C, fortran) recommended
Solid state theory graduate course recommended

Course ID

6183 WS 2011/12


Dr. Andrew Mitchell, Priv.-Doz. Dr. Ralf Bulla, Prof. Dr. Simon Trebst


Lucas Hollender, Etienne Gärtner

Information for participants

Orientation and course introduction:

Monday 5th March, 09:30 -- Seminar room of the Institute of Theoretical Physics, Cologne

Daily Schedule:

Please check the daily links on the left for detailed schedule and description of topics covered.

Rough Timetable:
09:30 -- 11:00: Lecture (seminar room of the institute of theoretical physics)
11:00 -- 11:15: Coffee
11:15 -- 12:30: Computer practical (Cip-Pool)
12:30 -- 13:30: Lunch
13:30 -- 15:00: Computer practical (Cip-Pool)
15:00 -- 15:30: Coffee
15:30 -- 17:00: Lecture (seminar room of the institute of theoretical physics)

Monday (05.03.2012)

09:30--11:00 Welcome and general introduction to computational methods and numerical techniques [SR THP]
11:15--12:00 Ising model and Monte Carlo [SR THP]
12:00--12:30 Computer practical [Cip-Pool]
12:30--13:15 Lunch break
13:15--16:00 Computer practical [Cip-Pool]
16:15--17:00 Ising model (summary); Quantum Monte Carlo [SR THP]

Tuesday (06.03.2012)

Basic toolbox for many-particle systems.
Non-interacting quantum systems: diagonalization by orthogonal transformation of operators, Green function methods, spectral functions, broadening discrete numerical data, Kramers-Kronig transformations etc.

Wednesday (07.03.2012)

Exact diagonalization of interacting quantum systems.
Lehmann representation of the spectral function.
Discretization schemes.

Thursday (08.03.2012)

Iterative diagonalization and truncation.
Logarithmic discretization, and the Numerical Renormalization Group (NRG).
Anderson impurity model.
Universality and scaling.

Friday (09.03.2012)

Exploiting entanglement, and the Density Matrix Renormalization Group (DMRG).
Introduction to the ALPS project.
Application to the Heisenberg model.