Teaching
'Mathematics for the Physical Sciences' (Undergraduate)
Course website and lecture materials can be found here (within Oxford)Sample exam papers can be found here (within Oxford)
- Wadham College: Thursdays 3--4pm in the PTCL Theory Annex
- Jesus Colelge: Thursdays 4--5pm in the PTC Theory Annex
Work to be handed in by 5pm on Wednesdays
'Numerical Methods for Many-Particle Systems' (Graduate)
Held at the Institute for Theoretical Physics, University of Cologne (March 2012).In conjunction with the Bonn-Cologne Graduate School of Physics and Astronomy.
Lecturers
Dr. Andrew Mitchell, Priv.-Doz. Dr. Ralf Bulla, Prof. Dr. Simon TrebstCourse Summary
This intensive course is intended to provide both a working understanding and real hands-on experience with the essential numerical techniques of solid state many-body physics.Rather than a 'black-box' philosophy, the course aims to discuss the theory and physics underpinning numerical approaches. Lectures will introduce models of central importance, such as the Ising model, the Anderson impurity model, the Hubbard model and the Heisenberg model. Using these as concrete examples, the Monte Carlo, Exact Diagonalization, Numerical Renormalization Group and Density Matrix Renormalization Group techniques will be discussed. Students will also gain supervised practical hands-on experience writing, using and modifying simple computer codes to solve real problems.
Schedule
Lecture 1: Introduction to many particle methods. Ising model and Monte Carlo.Computer practical: Monte Carlo for the classical Ising model.
Lecture 2: Basic toolbox for many-particle quantum systems.
Non-interacting quantum systems: diagonalization by orthogonal transformation of operators, calculation of physical quantities.
Lecture 3: Quantum Monte Carlo.
Computer practical: Basic toolbox for quantum systems.
Lecture 4: Green function methods, spectral functions, broadening discrete numerical data, Kramers-Kronig transformations etc.
Lecture 5: Exact diagonalization for intereacting quantum systems. Hubbard model.
Computer practical: Exact diagonalization for the 1d Hubbard model. Calculations of spectral functions.
Lecture 6: Discretization / coarse-graining methods. Quantum impurity problems.
Lecture 7: Numerical Renormalization Group (NRG).
Computer practical: NRG for the Anderson model.
Lecture 8: Renormalization and universality in the Kondo problem.
Lecture 9: Introduction to the ALPS project. Density Matrix Renormalization Group (DMRG).
Computer practical: DMRG for Heisenberg models.
Lecture 10: Summary of numerical methods for many-particle systems.