# Dimerization and N\'eel order in different quantum spin chains through a shared loop representation

Aizenman Michael
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Abstract:

The ground states of the spin-$S$ antiferromagnetic chain $H_\textrm{AF}$ with a projection-based interaction and the spin-$1/2$ XXZ-chain $H_\textrm{XXZ}$ at anisotropy parameter $\Delta=\cosh(\lambda)$ share a common loop representation in terms of a two-dimensional functional integral which is similar to the classical planar \$Q...More

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