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For the line of critical antiferromagnetic XXZ chains with coupling $J>0$ andanisotropy $0<\Delta \leq 1$, we describe how the block-spin renormalizationprocedure preserving the $SU_q(2)$ symmetry introduced by Martin-Delgado andSierra [Phys. Rev. Lett. 76, 1146 (1996)] can be reformulated as thetranslation-invariant scale-invariant Tree-Tensor-State of the smallestdimension that is compatible with the quantum symmetries of the model. Theproperties of this Tree-Tensor-State are studied in detail via the ground-stateenergy, the magnetizations and the staggered magnetizations, as well as theShannon-Renyi entropies characterizing the multifractality of the components ofthe wave function.

On the simplest scale invariant Tree-Tensor-States preserving the quantum symmetries of the antiferromagnetic XXZ chain