# Computational Many-Body Physics
summer 2018

Mon 14.00 - 15.30 | **E0.03**THP

Wed 16.00 - 17.30 |

**E0.03**THP

## 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- phase transitions: percolation, Ising model, finite-size scaling
- description of (frustrated) magnetism: Ising/Heisenberg/Kitaev models
- Monte Carlo sampling: sampling, error analysis, cluster updates, extended ensembles
- quantum Monte Carlo: world-line, variational, and probably auxiliary field techniques
- machine learning: supervised and unsupervised learning, neural networks, restricted Boltzmann machines
- exact diagonalization
- entanglement, matrix product states, DMRG, tensor network approaches

## Tutorials

Tutorials will be held every other week (in one of the lecture time slots). We will start on**Wednesday, April 18th**. The exercise sheets, which will be coordinated by Jan Attig, will guide you through small projects implementing and applying some of the numerical methods discussed in the lecture.

**Assignments**

- sheet 0: Julia warm up [notebook], Plotting in Julia [notebook], Twin prime numbers
- sheet 1: Percolation
- sheet 2: Lattices, Classical spin models, Percolation (cont'd) [solutions]
- sheet 3: Simulated Annealing, Cluster Updates, Extended Ensembles
- sheet 4: Digit Recognition, Phase Recognition in the Ising model, Tensor Flow
- sheet 5: Band structure calculations
- sheet 6: Molecular Dynamics — from molecules to galaxies

## 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

**General textbooks**

- 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

**Specialized literature**

- D.P. Landau and K. Binder, A Guide to Monte Carlo Simulations in Statistical Physics, Cambridge University Press (2005)

available in physics student library, university library - J. Gubernatis, N. Kawashima, P. Werner, Quantum Monte Carlo Methods, Cambridge University Press (2016)

available in physics student library, university library - Michael Nielsen, Neural Networks and Deep Learning
- J. Oitmaa, C. Hamer, W. Zheng, Series Expansion Methods, Cambridge University Press (2006)

## Prerequisites

The course is intended for master students; it builds on a bachelor level introduction to computational physics as it is taught in many places around the world. If you have not taken such a course, take a look at a recent version of such an introductory course by our group, e.g. Computer-Physik 2016.We do expect you to have

**light programming experience**, preferably in Julia (which we have been teaching since summer 2016 in the undergraduate course).