Seminar: Introduction to Quantum Spin Systems

MAT290-25, CRN 30216, Winter 2011, Mondays 1:10-2pm in MSB 2112.

The seminar will provide an elementary introduction to the theory of quantum spin systems for beginning graduate students and attempt the answer such questions as `What are quantum spin systems?', `Why do we study them?' and `What kind of research on this topic is going on at the moment?'.

Seminar Notes

Notes for 01/03/2011
Notes for 01/10/2011
Notes for 01/19/2011
Notes for 01/24/2011, also see the more detailed notes on SU(2) by Shannon Starr.
Notes for 01/31/2011 (Amanda's talk on the AKLT model).
Notes for 02/07/2011

References

(this list will grow over the course of the quarter):

Quantum Spin Systems, Bruno Nachtergaele, Article in the Encyclopedia of Mathematical Physics (Elsevier) arXiv:math-ph/0409006.

Quantum Spin Systems after DLS1978, Bruno Nachtergaele, in Spectral Theory and Mathematical Physics: A Festschrift in Honor of Barry Simon's 60th Birthday, Fritz Gesztesy et al. (Eds), Proceedings of Symposia in Pure Mathematics, Vol 76, part 1, pp 47--68, AMS, 2007. arXiv:math-ph/0603017.

Lieb-Robinson Bounds in Quantum Many-Body Physics, Bruno Nachtergaele and Robert Sims, in Entropy and the Quantum, Robert Sims and Daniel Ueltschi (Eds), Lecture Notes for the Arizona School of Analysis with Applications, 16-20 March 2009, Tucson, Arizona. Contemporary Mathematics, volume 529, American Mathematical Society (2010) pp 141-176. arXiv:1004.2086.

An annotated bibliography on the Heisenberg and related models, compiled by Tom Kennedy and Bruno Nachtergaele:The Heisenberg Model Bibliography.

Operator algebras and quantum statistical mechanics, O. Bratteli and D. W. Robinson, 2 ed., vol. 1 & 2, Springer Verlag, 1987 & 1997. See Ola Bratteli's webpage for downloadable pdfs.