Lecture: Computational Many-Body Physics
Summer Term 2016
Monday 14:00 - 15:30,
Seminarraum Theorie (old theory building)
Wednesday 14:00 - 15:30,
Konferenzraum 0.01 TP (new theory building)
This lecture gives an introduction to numerical methods
for the investigation of classical and quantum many-particle
systems. The focus in on models of strongly correlated
electron systems, such as the Hubbard model and the
single-impurity Anderson model. The physical phenomena
(Mott transitions, Kondo physics, etc.) these models are
supposed to describe, are quite often out of the reach of
analytical techniques - this triggered the development
of very powerful numerical approaches, see Sec. 3 in the
table of contents.
The lecture also includes a brief introduction to basic
theoretical concepts, such as Green functions and
continued fraction expansions, which are essential to
relate the numerical results to actual physical quantities
(see Sec. 2).
Module description
of the primary area of specialization
`Solid State Theory/Computational Physics'
Contents:
- Introduction
1.1 Many-Particle Systems in Solid State Theory
1.2 Strongly Correlated Electron Systems: the Basic Models
1.3 Physical Quantities
- Quantum Many-Particle Systems: Basics
2.1 Single-Particle and Many-Particle Spectra
2.2 Green Functions
- Quantum Many-Particle Systems: Methods
3.1 Exact Diagonalization
3.2 Numerical Renormalization Group
3.3 Density-Matrix Renormalization Group
3.4 Quantum Monte Carlo
script
Literature:
Here is a selection of review articles, covering the topics in Section 3:
3.2 Numerical Renormalization Group
3.3 Density-Matrix Renormalization Group
The Autumn School on Correlated Electrons, held every year at the
Forschungszentrum Jülich, contains lots of useful overview
articles on many-body techniques which are all available online.
Tutorials:
Wednesdays, 14:00 - 15:30, every second week
Dates: April 20, May 4, May 25, June 8, June 22, July 6, July 20
Konferenzraum 0.01 TP (new theory building)
Tutor: Christopher Bartel
The exercise sheets contain both analytical and programming
exercises. We recommend to use the python programming language
(templates for some of the exercises will be provided).
Exercises:
Solutions can be returned in groups of up to three students (please
use the letter box in front of the entrance to the theory institute -
old building).
The computer codes should be sent via e-mail to Christopher Bartel.
Requirements for the admission to the module exam:
- primary and secondary area of specialization:
- active participation in the tutorials
- at least 50% of the points from the exercises
- elective subject:
- active participation in the tutorials
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