Lecture: Computational ManyBody 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)
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 manyparticle
systems. The focus in on models of strongly correlated
electron systems (Hubbard model,
singleimpurity 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'
Contents:
 Introduction
1.1 manyparticle systems in solid state theory
1.2 the basic models
1.3 physical quantities  Quantum ManyParticle Systems: Basics
2.1 singleparticle and manyparticle spectra
2.2 Green functions
2.3 reduced density matrix and entanglement  Quantum ManyParticle Systems: Methods
3.1 Exact Diagonalization
3.2 Numerical Renormalization Group
3.3 DensityMatrix Renormalization Group
3.4 Quantum Monte Carlo
Literature:
Here is a selection of review articles, covering the topics in Section 3:
3.2 Numerical Renormalization Group
Here is a selection of review articles, covering the topics in Section 3:
3.2 Numerical Renormalization Group

R. Bulla, T.A. Costi, and Th. Pruschke
Numerical renormalization group method for quantum impurity systems
Rev. Mod. Phys. 80, 395 (2008)
 U. Schollwöck
The densitymatrix renormalization group
Rev. Mod. Phys. 77, 259 (2005)
Tutorials:
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).
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).