- Sheet 0 (download also the Python Cheat Sheet) - Discussion: April, 27.
- Sheet 1 (download also the following Python script) - Discussion: May, 4.
- Sheet 2 - Discussion: May, 11.
- Sheet 3 - Discussion: May, 18.
- Sheet 4 - Discussion: June, 1 (covers 2 weeks).
- Sheet 5 - Discussion: June, 8.
- Sheet 6 - Discussion: June, 22 (covers 2 weeks).
- Sheet 7 - Discussion: June, 29.
- Sheet 8 - Discussion: July, 6.
- Sheet 9 - Discussion: July, 13.
- Sheet 10 - Discussion: July, 20 (last sheet).
Take-home final exam: Exam Sheet
- Instructions: the exam consists on two exercises. In order to pass, you need to solve and present >30% of them, best grades will be given for >60%.
- Oral exam: August 11, 8:30 (sharp!), Room: 5.0.20 (new room!)
Oral examination will be held individually and will have an approximate duration of 20-25 minutes. Please, have available all the relevant material for discussion of your exam results (plots properly labelled (!), relevant code, observations, etc.). You can print out this material or bring it in your laptop. Please, be on time for your scheduled appointment. Best of luck!
- Ansgar Graf, 8:30-8:55
- Wolfgang Hogger, 9:00-9:25
- Thomas Naimer, 9:30-9:55
- Jakob Schlör, 10:00-10:25
This course presumes basic knowledge of quantum mechanics and solid state physics. Practice requires light programming experience in Python, C++ or other programming language.
The advent of powerful algorithms – like Krylov-subspace methods,
the Kernel-polynomial 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 of complex physical phenomena.
This lecture offers an introduction into basic computational techniques
and the conceptual ideas behind them. 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 the exercises, practical
implementations with Python for scientifically relevant examples
will be given.
The course will proceed along the following roadmap:
1. The Gas of Non-interacting Fermions
1.1 Free fermions, state counting, band structure
1.2 Tight binding models – graphene
(Fast fourier transformation)
1.3 Topologically non-trivial 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: Fermi-Liquid-Theory
3.2 Hartree-Fock method (HF)
(Self-consistent iteration schemes)
(Kernel-Polynomial Method and stochastic trace evolution)
3.4 Interaction effects on quantum dynamics – Time dependent HF and random phase approximation
(Kubo-formalism and theory of linear response)
3.5 Excursion into superconductivity: BCS and Boguliubov-deGennes theory
(modelling topological superconductors, Majorana edge modes, Kitaev models)
4. Statistical and Transport Physics
4.1 Hydrodynamics and classical transport
(Partial differential equations, difference equations, boundary problems)
4.2 Quantum transport
(Transfer matrix technique and Landauer formalism)
4.3 Molecular Electronics
(Non-equilibrium Green's functions)
4.4. (Thermal) phase transitions – Ising transition
(Monte-Carlo simulations and finite size scaling)
4.5 Quantum phase transitions - Anderson transition
(Fractal and Multifractal analysis)
5. Strongly Correlated Electron Systems
5.1 Briefing: Kondo effect
5.2 The numerical renormalization group (NRG)
5.3 Briefing: Luttinger liquid
5.4 The density matrix renormalization group method (DMRG)
Cambridge university Press (2007)
- An introduction to Computational Physics,
Cambrdige University Press (2006)
- Matrix Computations
G. H. Golub, C. F. van Loan
The Johns Hopkins University Press, Baltimore London (1996)
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)