Numerical methods for many-particle systems - part I: basics

Mi, 16:00- 17:30; Do. 16:00- 17:30
Seminarraum des Instituts für Theoretische Physik


Basic numerical methods and concepts for the investigation of quantum-mechanical many-particle systems. One of the topics is the calculation of the Green functions of correlated fermionic and bosonic systems. Part II of the lecture will deal with more advanced methods such as quantum Monte-Carlo, numerical renormalization group, etc.

The lecture is aiming at students with some background in quantum-field theory; experience with modern programming languages (c, fortran, ...) is useful, but not absolutely necessary.


I. Single-particle and many-particle spectra

I.1 a single level

I.2 many levels (no interactions)

I.3 tight-binding models

two-site model, one-dimensional chain (periodic and open boundary conditions), diagonalization of the Hamiltonian versus diagonalization of the Hamiltonian matrix, diagonalization via Fourier-Transformation, density of states

II. Green functions

II.1 some definitions

imaginary-time Green function G(tau), spectral function A(omega), how to calculate A(omega) from a given G(tau)

II.2 Green functions for the single-impurity Anderson model

II.3 broadening of discrete spectral functions

II.4 continued fraction expansion

III Exact diagonalization of small clusters

III.1 general remarks

III.2 single-impurity Anderson model

III.3 Hubbard model

III.4 spin-boson model

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