Twisted XXZ even-chain norm conjecture

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Let ∣Ψ(2n)⟩|\Psi^{(2n)}\rangle be the normalized ground-state vector of the twisted XXZ chain with 2n2n sites, let

N2n2=⟨Ψ(2n)∣Ψ(2n)⟩,\mathcal N_{2n}^2=\langle\Psi^{(2n)}|\Psi^{(2n)}\rangle,

and let AnA_n be the number of alternating-sign n×nn\times n matrices. The twisted XXZ even-chain norm conjecture. The squared norm is

N2n2=2⋅5⋯(3n−1)1⋅4⋯(3n−2)An2.\mathcal N_{2n}^2=\frac{2\cdot5\cdots(3n-1)}{1\cdot4\cdots(3n-2)}A_n^2.

The formula is presented as an analogue of an earlier periodic-chain conjecture and remains unproved in the supplied text.

References

Primary source

A. V. Razumov and Yu. G. Stroganov, “Spin chains and combinatorics: twisted boundary conditions”, arXiv:cond-mat/0102247 (2001).

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