Dresden 2014 – scientific programme

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TT: Fachverband Tiefe Temperaturen

TT 4: Low-Dimensional Systems: 1D - Theory

TT 4.6: Talk

Monday, March 31, 2014, 10:45–11:00, HSZ 201

The Cirac-Sierra construction and long range SU(N) spin models — Roberto Bondesan and •Thomas Quella — University of Cologne, Cologne, Germany

The Haldane-Shastry model for SU(2) is a paradigmatic example of a long range spin chain. The model is remarkable in that it allows for the analytic determination of the complete energy spectrum and explicit expressions for the associated wave functions. Besides being relevant in the context of fractional quantum Hall physics, it also provides a discretization of the critical SU(2) Wess-Zumino-Witten (WZW) conformal field theory.

Recently, Cirac and Sierra found a conceptually new and intriguing perspective on long range spin chains by reverting the previous idea. Now long range spin models arise as parent Hamiltonians of a given WZW correlator. This construction provides a generalization of the Haldane-Shastry model in the sense that the symmetry group, the representations and the positions of the spins may be freely chosen. It even permits the construction of 2D models with a specific groundstate wave function.

In this talk, we apply this construction to different types of SU(N) spin models and discuss the physical implications.