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In this article, we construct the axialvector-diquark-axialvector-antidiquarktype tensor current to interpolate both the vector and axialvector tetraquarkstates, then calculate the contributions of the vacuum condensates up todimension-10 in the operator product expansion, and obtain the QCD sum rulesfor both the vector and axialvector tetraquark states. The numerical resultssupport assigning the $Z_c(4020/4025)$ to be the $J^{PC}=1^{+-}$diquark-antidiquark type tetraquark state, and assigning the $Y(4660)$ to bethe $J^{PC}=1^{--}$ diquark-antidiquark type tetraquark state. Furthermore, wetake the $Y(4260)$ and $Y(4360)$ as the mixed charmonium-tetraquark states, andconstruct the two-quark-tetraquark type tensor currents to study the masses andpole residues. The numerical results support assigning the $Y(4260)$ and$Y(4360)$ to be the mixed charmonium-tetraquark states.

Tetraquark state candidates: $Y(4260)$, $Y(4360)$, $Y(4660)$ and $Z_c(4020/4025)$