Computational Many-Body Physics
summer 2015
Mon, Wed 16:00-17:30
seminar room | Institute for Theoretical Physics
Overview
The lecture will provide an overview of modern numerical approaches to many-body systems, both classical and quantum. The in-depth introduction of elementary algorithms will be complemented by application of these methods to fundamental models and phenomena, mostly arising in the context of condensed matter physics, but we might branch out to other fields as well.Syllabus
A tentative list of topics includes- percolation
- phase transitions
- finite-size scaling
- Monte Carlo sampling
- extended ensemble techniques
- molecular dynamics
- Hartree-Fock and density-functional methods
- exact diagonalization
- quantum Monte Carlo (world-line, variational, and probably auxiliary field techniques)
- series expansions
- numerical renormalization group
- density matrix renormalization group
- entanglement and tensor network approaches (PEPS, MERA)
Tutorials
Tutorials will be held every other week (in one of the lecture time slots, mostly Wednesdays). We will start on Wednesday, April 15th. The exercise sheets will guide you through small projects implementing and applying some of the numerical methods discussed in the lecture.Assignments
- sheet 0: Python warm-up
- sheet 1: Cython, percolation, Pauli percolation
- sheet 2: parallel programming with MPI, Metropolis algorithm for the Ising model
- sheet 3: nobody is perfect, extended ensemble simulations
- sheet 4: need for speed, molecular dynamics simulation of Argon gas
- sheet 5: Matrices are a snake's best friend, A quantum of Ising, Mastering exact diagonalization in 10 minutes or less
- sheet 6: Certainly uncertain, stochastic series expansion (SSE)
- sheet 7: density matrix renormalization group (DMRG)
Lectures
- week 01: percolation — combinatorial musings
- week 02: percolation — numerics, fractals, and finite-size scaling
- week 03: Monte Carlo simulations
- week 04: Ising model
- week 05: extended ensemble simulations
- week 06: molecular dynamics simulations
- week 07: Hartree-Fock and density functional theory
- week 08: exact diagonalization
- week 09: quantum Monte Carlo
- week 10: entanglement and DMRG
- week 11: series expansions
Mailing list
We have created a mailing list for this lecture, which will be used to send out further information regarding the lectures, exercise classes, and homework assignments.We ask all students to sign up for this mailing list.
Literature
- J.M. Thijssen, Computational Physics, Cambridge University Press (2007)
available in physics student library, university library - Tao Pang, An Introduction to Computational Physics, Cambridge University Press (2006)
available in physics student library, university library - Werner Krauth, Statistical Mechanics: Algorithms and Computation, Oxford University Press (2006)
available in physics student library, university library