Lecture: Computational Many-Body Physics

summer term 2017

Wednesday, Sep 6, until Friday, Sep 29
10:00 - 11:30 and 13:00 - 14:30
Konferenzraum 0.01 TP (new theory building)
This lecture gives an introduction to numerical methods for the investigation of quantum many-particle systems. The focus in on models of strongly correlated electron systems (Hubbard model, single-impurity Anderson model) and quantum spin models (Heisenberg model, Kitaev model). The physical phenomena (Mott transitions, Kondo physics, spin liquid 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, continued fraction expansions, reduced density matrices, entanglement measures (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 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
    2.3 reduced density matrix and entanglement
  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.

The exercise sheets contain both analytical and programming exercises. We recommend to use the Julia programming language (templates for some of the exercises will be provided).