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Advanced numerical methods in many-body physics



This is a course about modern computational methods for the simulation of many-body systems in condensed matter physics, including systems from classical statistical physics and quantum many-body problems. Besides the theoretical understanding of these algorithms and the physics of many-body systems an important part of the course is to gain practical experience in computational physics by implementing algorithms (programming) and performing simulations.


Recommended for people who:

*     would like to dive into the fascinating field of computational physics

*     would like to learn about state-of-the-art methods relevant in many areas in Science (also in non-academic areas)

*     intend to do a computationally oriented project in future (e.g. Master- or PhD-thesis)

*     would like to strengthen their understanding in many-body physics

*     enjoy programming and would like to get more practice in programming (we use Python in the exercises)



*     Monte Carlo methods for classical spin systems (Metropolis algorithm, cluster algorithms and flat-histogram methods)

*     Numerical study of first and second order phase transitions in magnetic systems

*     Numerical methods for the quantum one-body problem

*     Quantum many-body problems (electronic structure problem) and effective lattice models (e.g. spin chains and Hubbard model)

*     Hartree-Fock and Density Functional Theory

*     Exact diagonalization of quantum lattice models

*     Quantum Monte Carlo and the negative sign problem

*     The density matrix renormalization group and tensor network methods


Programming language:

*     As programming language we will use Python

*     We will do a short introduction/warm-up in the first week
(see slides part I, and part II)


This course (6EC) takes place in block 5 (semester 2), see course catalogue or datanose.