# Quantum spin systems on infinite lattices

November 12, 2013

These are the lecture notes for a one semester course at Leibniz University
Hannover. The main aim of the course is to give an introduction to the
mathematical methods used in describing discrete quantum systems consisting of
infinitely many sites. Such systems can be used, for example, to model some
materials in condensed matter physics or lattice gases.
The contents are roughly as follows: (1) quick recap of essentials from
functional analysis, (2) introduction to operator algebra, (3) algebraic
quantum mechanics, (4) infinite systems (quasilocal algebra), (5) KMS and
ground states, (6) Lieb-Robinson bounds, (7) short discussion on related topics
for further reading.
The level is aimed at students who have at least had some exposure to
(functional) analysis and have a certain mathematical "maturity".

Keywords:

lectures