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

Aizenman Michael
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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