Lecture: Computational ManyBody Physics
summer term 2017
daily from Wednesday, Sep 6, until Friday, Sep 29
10:00  11:30 (lectures) and 13:00  14:30 (tutorials)
Seminarraum 0.01 TP (new theory building)
(Wednesday, Sep 20, until Friday, Sep 22: Seminarraum Theorie in the old theory building)
10:00  11:30 (lectures) and 13:00  14:30 (tutorials)
Seminarraum 0.01 TP (new theory building)
(Wednesday, Sep 20, until Friday, Sep 22: Seminarraum Theorie in the old theory building)
Please note: The lecture consists of two parts. Part II (Sep 1829)
will be given by
Prof. S. Trebst.
The following description of content etc. refers to part I.
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:
Part II will cover the following topics:
 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
Part II will cover the following topics:
 percolation
MonteCarlo sampling
Ising model/cluster approaches
extended ensemble techniques
quantum MonteCarlo
entanglement
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).
Exercises: Please note: we recommend to go through all the exercise sheets, but in the tutorials the focus will be on the following exercises (this is a preliminary plan for the first eight tutorials):
 tutorial 1 (Sep 6): s1/ex1 singleparticle and manyparticle spectra, notebook
 tutorial 2 (Sep 7): s2/ex3 tightbinding chain; density of states; s2/ex4 spinmodels on a threesite cluster, notebook
 tutorial 3 (Sep 8): s3/ex5 Hamilton matrices for spin models; s4/ex4 the reduced density matrix, notebook
 tutorial 4 (Sep 11): s3/ex1 Hamilton matrix of the tightbinding chain, notebook
 tutorial 5 (Sep 12): s4/ex3 spin correlations of onedimensional spin models, notebook
 tutorial 6 (Sep 13): s5/ex4 reduced density matrix and entanglement entropy, notebook
 tutorial 7 (Sep 14): s6/ex1 entanglement entropy for onedimensional spin models
 tutorial 8 (Sep 15): s5/ex3 Lanczos algorithm, notebook
Spinconventions.ipynb
Sheet 5  Exercise 1
Sheet 5  Exercise 2
2D_Ising_Notes.pdf, 2D_Ising_Notes.ipynb
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).
Exercises: Please note: we recommend to go through all the exercise sheets, but in the tutorials the focus will be on the following exercises (this is a preliminary plan for the first eight tutorials):
 tutorial 1 (Sep 6): s1/ex1 singleparticle and manyparticle spectra, notebook
 tutorial 2 (Sep 7): s2/ex3 tightbinding chain; density of states; s2/ex4 spinmodels on a threesite cluster, notebook
 tutorial 3 (Sep 8): s3/ex5 Hamilton matrices for spin models; s4/ex4 the reduced density matrix, notebook
 tutorial 4 (Sep 11): s3/ex1 Hamilton matrix of the tightbinding chain, notebook
 tutorial 5 (Sep 12): s4/ex3 spin correlations of onedimensional spin models, notebook
 tutorial 6 (Sep 13): s5/ex4 reduced density matrix and entanglement entropy, notebook
 tutorial 7 (Sep 14): s6/ex1 entanglement entropy for onedimensional spin models
 tutorial 8 (Sep 15): s5/ex3 Lanczos algorithm, notebook
Spinconventions.ipynb
Sheet 5  Exercise 1
Sheet 5  Exercise 2
2D_Ising_Notes.pdf, 2D_Ising_Notes.ipynb
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