Quantum incompressibility and Razumov Stroganov type conjectures

Details Quantum incompressibility and Razumov Stroganov type conjectures Quantum incompressibility and Razumov Stroganov type conjectures

2005-06-03

arxiv.org/abs/cond-mat/0506075v1

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

latex ihp.tex, 2 files, 1 figure, 28 pages (http://www-spht.cea.fr/articles/T05/087)

Scientific paper

10.1007/s00023-005-0254-4

We establish a correspondence between polynomial representations of the Temperley and Lieb algebra and certain deformations of the Quantum Hall Effect wave functions. When the deformation parameter is a third root of unity, the representation degenerates and the wave functions coincide with the domain wall boundary condition partition function appearing in the conjecture of A.V. Razumov and Y.G. Stroganov. In particular, this gives a proof of the identification of the sum of the entries of a O(n) transfer matrix eigenvector and a six vertex-model partition function, alternative to that of P. Di Francesco and P. Zinn-Justin.

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