For integer-spin chains with SO(3) and translation symmetry, the minimal Renyi entropy is the smaller of two explicit expressions, and zero correlation length is forbidden.
So far we can only prove this statement for the special case where α = 1 (see Appendix A), but we are unable to prove or disprove it for other values of α
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Symmetry-enforced minimal entanglement and correlation in quantum spin chains
For integer-spin chains with SO(3) and translation symmetry, the minimal Renyi entropy is the smaller of two explicit expressions, and zero correlation length is forbidden.