Lecture: Computational Many-Body Physics

apl. Prof. Dr. Ralf Bulla

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'

  1. Introduction
    1.1 Many-Particle Systems in Solid State Theory
    1.2 Strongly Correlated Electron Systems: the Basic Models
    1.3 Physical Quantities
  2. Quantum Many-Particle Systems: Basics
    2.1 Single-Particle and Many-Particle Spectra
    2.2 Green Functions
  3. 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


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.

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:

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