Exercise sheets
Sheet 0,
discussion: April 8,
download also the
Cheat sheet
Sheet 1,
discussion: April 14,
download also the python script
Sheet 2,
discussion: April 21
Sheet 3,
discussion: April 28
Sheet 4,
discussion:
Monday, May 9, 15:15—16:45 CIPPool PHY2
Solution: Sheet 4 / Problem 2 (Lanczos algorithm)
Sheet 5,
discussion: May 12
Sheet 6,
discussion: May 19
Sheet 7,
discussion: June 2
Quick guide to FHIAIMS;
you can also download the
AIMS lecture,
given on May 20
Sheet 8,
discussion: June 9,
BenzeneExample.xyz,
pentacene.geometry.in
Sheet 9,
discussion: June 16
New location of FHIAIMS files and executables: /temp/ccmt/software/
The old location is obsolete.
Sheet 10,
discussion: June 23
Sheet 11,
discussion: June 30 in an
extraordinary location PHY 1.0.02
Sheet 12,
discussion: July 7 (this is the last sheet)
Final Exam
Takehome final exam: Exam sheet
Important information
 Deadline for submission of numerical results: August 12
Results should be submitted in a single .pdf file by email to Dr. Daniel Hernangómez Pérez. You can use your favorite document preparation tool (LaTeX recommended). Please make an effort so that the document is clear and readable (sections, subsections etc.), label all plots accordingly and add the most important parts of your code integrated into the solutions with comments and explanations.
Note: if email submission is impossible for you, we can arrange hard copy submissions by request.
 Oral exam: September 26, 9:30 (sharp!)  11:00, Room PHY 4.1.13
Oral examination will be held individually and will have an approximate duration of 20 minutes. Please, be on time to your scheduled appointment. Best of luck!
 Hubert Beck, 9:30  9:50
 Andreas Hauke, 9:50  10:10
 Thomas Karl, 10:10  10:30
 Fabian Stöger, 10:30  10:50
Contact person: Dr. Daniel Hernangómez Pérez, daniel.hernangomez(at)ur.de, office PHY 3.1.24
Contents
The advent of powerful algorithms – like Krylovsubspace methods,
the Kernelpolynomial method or recursive Green's function methods, ...–
together with the improving computer power has opened up a completely
new route to test existing concepts and to obtain new insights into
broad classes of physical systems. Nowadays, computational tools are
well established in all branches of theoretical sciences and make unique
and indispensable contributions. Indeed, often they provide the only
route for systematic studies and improved understanding.
This lecture offers an introduction into basic computational techniques
and the conceptual ideas behind. The pedagogical approach of the lecture
will be to start from a fundamental example, usually taken from the
physical sciences, and then develop a
numerical approach starting from there. In exercises practical
implementations with Python for scientifically relevant examples
will be given.
The lecture will proceed along the following roadmap:
1. The Gas of Noninteracting Fermions
1.1 Free fermions, state counting, band structure
1.2 Tight binding models – graphene
(Fast fourier transformation)
1.3 Excursion: Topologically nontrivial materials
2. Beyond Band Structure Physics
2.1 Broken translational symmetries – Hofstadter butterfly
(Full matrix routines, LAPACK)
2.2 Disorder effects
(General purpose numerics: iterative methods, linear solvers)
2.3 Wavepacket propagation in nanostructures
(Sparse matrix methods: Krylov subspace technology)
2.4 Ground states
(Lanczos and Davidson methods)
3. Interaction Effects  Mean Field Theories
3.1 Briefing: FermiLiquidTheory
3.2 HartreeFock method (HF)
(Selfconsistent iteration schemes)
3.3 Thermodynamics
(KernelPolynomial Method and stochastic trace evolution)
3.4 Interaction effects on quantum dynamics – Time dependent HF and random phase approximation
(Kuboformalism and theory of linear response)
3.5 Superconductivity: BCS and BoguliubovdeGennes theory
(Topological superconductors, Majorana edge modes, Kitaev models)
4. Density Functional Theory (DFT)
4.1 Basic idea and Levi's proof
4.2 Exact properties
4.3 Exensions of DFT: SpinDFT, time dependent DFT etc.
4.4 Approximate functionals
4.5 Beyond DFT: GWtheory
5. Statistical and Transport Physics
5.1 Hydrodynamics and classical transport
(Partial differential equations, difference equations, boundary problems)
5.2 Quantum transport
(Transfer matrix technique and Landauer formalism)
5.3 Molecular Electronics
(Nonequilibrium Green's functions)
5.4. (Thermal) phase transitions – Ising transition
(MonteCarlo simulations and finite size scaling)
5.5 Quantum phase transitions  Anderson transition
(Fractal and Multifractal analysis)
6. Strongly Correlated Electron Systems
6.1 Briefing: Kondo effect
6.2 The numerical renormalization group
6.3 Briefing: Luttinger liquid
6.4 The density matrix renormalization group method
Literature: Computational Methods

Computational Physics,
J.M. Thijsen,
Cambridge university Press (2007)
 An introduction to Computational Physics,
Tao Pang
Cambrdige University Press (2006)
 Matrix Computations
G. H. Golub, C. F. van Loan
The Johns Hopkins University Press, Baltimore London (1996)
Literature: Conceptual framework of modern condensed matter physics
 Principles of condensed matter systems
P. M. Chaikin and T.V. Lubensky,
Cambridge, University Press (1995)
 Condensed Matter Field Theory,
A. Altland and B. Simons
Cambridge University Press (2010)
 Quantum Theory of the Electron Liquid
G. Giuliani G. Vignale
Cambridge, University Press (2005)
 Basic notions of Condensed Matter Physics,
P.W. Anderson, 'Frontiers in Physics'
Benjamin / Cummings Publishing Company (1984)