Twisted XXZ next-nearest-neighbour correlation conjecture

From papers

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

O2n=Ψ(2n)OΨ(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+22n=71n419n2+2016(4n21)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.

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Sources & referencesView supporting material

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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