Lecture: Computational Many-Body Physics
Summer Term 2014
Monday, 14:00 - 15:30 and
Wednesday 16:00 - 17:30
seminar room of the theory institute
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).
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
3.5 Dynamical Mean-Field Theory
- Classical Many-Particle Systems
4.1 Ising Model
4.2 Fermi-Pasta-Ulam Problem
4.3 Gravitating N-Body Problems
Literature:
Tutorials:
Wednesdays, 16:00 - 17:30, every second week
Dates: April 16, April 30, May 14, June 2, June 18, July 2, July 16
Seminarraum Theorie
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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