Monday, 14:00 - 15:30 and Wednesday 16:00 - 17:30

seminar room of the theory institute

This lecture gives an introduction to numerical methods for the investigation of classical and quantum many-particle systems. The focus in on models of strongly correlated electron systems, such as the Hubbard model and the single-impurity Anderson model. The physical phenomena (Mott transitions, Kondo physics, etc.) these models are supposed to describe, are quite often out of the reach of analytical techniques - this triggered the development of very powerful numerical approaches, see Sec. 3 in the table of contents. The lecture also includes a brief introduction to basic theoretical concepts, such as Green functions and continued fraction expansions, which are essential to relate the numerical results to actual physical quantities (see Sec. 2).

- Introduction

1.1 Many-Particle Systems in Solid State Theory

1.2 Strongly Correlated Electron Systems: the Basic Models

1.3 Physical Quantities - Quantum Many-Particle Systems: Basics

2.1 Single-Particle and Many-Particle Spectra

2.2 Green Functions - Quantum Many-Particle Systems: Methods

3.1 Exact Diagonalization

3.2 Numerical Renormalization Group

3.3 Density-Matrix Renormalization Group

3.4 Quantum Monte Carlo

3.5 Dynamical Mean-Field Theory - Classical Many-Particle Systems

4.1 Ising Model

4.2 Fermi-Pasta-Ulam Problem

4.3 Gravitating N-Body Problems

- R. Bulla, T.A. Costi, and Th. Pruschke

Numerical renormalization group method for quantum impurity systems

Rev. Mod. Phys. 80, 395 (2008) - U. Schollwöck

The density-matrix renormalization group

Rev. Mod. Phys. 77, 259 (2005)

Wednesdays, 16:00 - 17:30, every second week

Dates: April 16, April 30, May 14, June 2, June 18, July 2, July 16

Seminarraum Theorie

Requirements for the admission to the module exam

- primary and secondary area of specialization:
- active participation in the tutorials
- at least 50% of the points from the exercises

- elective subject:
- active participation in the tutorials

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