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A search for the pair-production of vector-like quarks optimized for decaysinto a $Z$ boson and a third-generation Standard Model quark is presented,using the full Run 2 dataset corresponding to 139 fb$^{-1}$ of $pp$ collisionsat $\sqrt{s}=13$ TeV, collected in 2015-2018 with the ATLAS detector at theLarge Hadron Collider. The targeted final state is characterized by thepresence of a $Z$ boson with high transverse momentum, reconstructed from apair of same-flavour leptons with opposite-sign charges, as well as by thepresence of $b$-tagged jets and high-transverse-momentum large-radius jetsreconstructed from calibrated smaller-radius jets. Events with exactly two orat least three leptons are used, which are further categorized by the presenceof boosted $W$, $Z$, and Higgs bosons and top quarks. The categorization isperformed using a neural-network-based boosted object tagger to enhance thesensitivity to signal relative to the background. No significant excess abovethe background expectation is observed and exclusion limits at 95% confidencelevel are set on the masses of the vector-like partners $T$ and $B$ of the topand bottom quarks, respectively. In the singlet model, the limits allow $m_T >1.27$ TeV and $m_B > 1.20$ TeV. In the doublet model, allowed masses are $m_T >1.46$ TeV and $m_B >1.32$ TeV. In the case of 100% branching ratio for$T\rightarrow Zt$ and 100% branching ratio for $B\rightarrow Zb$, the limitsallow $m_T > 1.60$ TeV and $m_B > 1.42$ TeV, respectively.

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Search for pair-production of vector-like quarks in $pp$ collision  events at $\sqrt{s}=13$ TeV with at least one leptonically decaying $Z$ boson  and a third-generation quark with the ATLAS detector