Supersymmetry on Jacobstahl lattices

Details Supersymmetry on Jacobstahl lattices Supersymmetry on Jacobstahl lattices

2005-10-11

arxiv.org/abs/cond-mat/0510272v1

J.Phys. A38 (2005) L809-L814

Physics

Condensed Matter

Statistical Mechanics

6 pages, 0 figures

Scientific paper

10.1088/0305-4470/38/48/L01

It is shown that the construction of Yang and Fendley (2004 {\it J. Phys. A: Math.Gen. {\bf 37}} 8937) to obtainsupersymmetric systems, leads not to the open XXZ chain with anisotropy $\Delta =-{1/2}$ but to systems having dimensions given by Jacobstahl sequences.For each system the ground state is unique. The continuum limit of the spectra of the Jacobstahl systems coincide, up to degeneracies, with that of the $U_q(sl(2))$ invariant XXZ chain for $q=\exp(i\pi/3)$. The relation between the Jacobstahl systems and the open XXZ chain is explained.

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