The quantum symmetric XXZ chain at Delta=-1/2, alternating sign matrices and plane partitions

Details The quantum symmetric XXZ chain at Delta=-1/2, alternating sign matrices and plane partitions The quantum symmetric XXZ chain at Delta=-1/2, alternating sign matrices and plane partitions

2001-01-25

arxiv.org/abs/cond-mat/0101385v1

J.Phys.A 34 (2001) L265-L270

Physics

Condensed Matter

Statistical Mechanics

7 pages, Latex

Scientific paper

10.1088/0305-4470/34/19/101

We consider the groundstate wavefunction of the quantum symmetric antiferromagnetic XXZ chain with open and twisted boundary conditions at $\Delta=-{1/2}$, along with the groundstate wavefunction of the corresponding O($n$) loop model at $n=1$. Based on exact results for finite-size systems, sums involving the wavefunction components, and in some cases the largest component itself, are conjectured to be directly related to the total number of alternating sign matrices and plane partitions in certain symmetry classes.

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