  The impact of jet quenching on $Z^0$-tagged jets in relativistic heavy-ion
collisions at the Large Hadron Collider (LHC) is investigated. We employ Sharpa
Monte Carlo program that combines next-to-leading order matrix elements with
matched resummation of parton shower to compute the initial $Z^0$+jet
production. The Linear Boltzmann Transport (LBT) model is then used to simulate
the propagation, energy attenuation of and medium response induced by jet
partons in the quark-gluon plasma. With both higher-order corrections and
matched soft/collinear radiation as well as a sophisticated treatment of parton
energy loss and medium response in LBT, our numerical calculations can provide
the best description so far of all available observables of $Z^0$+jet
simultaneously in both p+p and Pb+Pb collisions, in particular, the shift of
the distribution in transverse momentum asymmetry $x_{\rm jZ}=p_T^{\rm
jet}/p_T^Z$, the modification of azimuthal angle correlation in
$\Delta\phi_{\rm{j}Z}=|\phi_{\rm jet}-\phi_Z|$ and the overall suppression of
average number of $Z^0$-tagged jets per boson $R_{\rm jZ}$ at $\sqrt s =5.02$
TeV as measured by the CMS experiment. We also show that higher-order
corrections to $Z^0$+jet production play an indispensable role in understanding
$Z^0$+jet azimuthal angle correlation at small and intermediate
$\Delta\phi_{\rm jZ}$, and momentum imbalance at small $x_{\rm jZ}$. Jet
quenching of the sub-leading jets is shown to lead to suppression of $Z^0$+jet
correlation at small azimuthal angle difference $\Delta\phi_{\rm jZ}$ and at
small $x_{\rm jZ}$.
