Quantum Spin Systems on Infinite Lattices
Abstract
This is an extended and corrected version of lecture notes originally written for a one semester course at Leibniz University Hannover. The main aim of the notes 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 the materials in condensed matter physics. The notes provide the necessary background material to access recent literature in the field. Some of these recent results are also discussed. 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) LiebRobinson bounds, (7) algebraic quantum field theory, (8) superselection sectors of the toric code, (9) HaagRuelle scattering theory in spin systems, (10) applications to gapped phases. The level is aimed at students who have at least had some exposure to (functional) analysis and have a certain mathematical "maturity".
 Publication:

Lecture Notes in Physics, Berlin Springer Verlag
 Pub Date:
 2017
 DOI:
 10.1007/9783319514581
 arXiv:
 arXiv:1311.2717
 Bibcode:
 2017LNP...933.....N
 Keywords:

 Physics;
 Mathematical Physics;
 Quantum Physics
 EPrint:
 To be published in Lecture Notes in Physics (Springer). v2: extended and corrected. 157 pages