Lecture: Computational Many-Body Physics

Priv.-Doz. Dr. Ralf Bulla

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).

  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
    3.5 Dynamical Mean-Field Theory
  4. Classical Many-Particle Systems
    4.1 Ising Model
    4.2 Fermi-Pasta-Ulam Problem
    4.3 Gravitating N-Body Problems


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

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