Twisted XXZ next-nearest-neighbour correlation conjecture

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For the even-site ground state ∣Ψ(2n)⟩|\Psi^{(2n)}\rangle, define the normalized expectation of an operator OO by

⟨O⟩2n=⟨Ψ(2n)∣O∣Ψ(2n)⟩⟨Ψ(2n)∣Ψ(2n)⟩,\langle O\rangle_{2n}=\frac{\langle\Psi^{(2n)}|O|\Psi^{(2n)}\rangle}{\langle\Psi^{(2n)}|\Psi^{(2n)}\rangle},

and define αi=(1+σiz)/2\alpha_i=(1+\sigma_i^z)/2. The twisted XXZ next-nearest-neighbour correlation conjecture.

⟨αiαi+2⟩2n=71n4−19n2+2016(4n2−1)2.\langle\alpha_i\alpha_{i+2}\rangle_{2n}=\frac{71n^4-19n^2+20}{16(4n^2-1)^2}.

This is the twisted-boundary analogue of an earlier correlation conjecture; the source states that it is open at this point.

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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