  The zirconium isotopes with $A=$ 92$-$110 have one of the most complicated
evolution of structure in the nuclear chart. In order to understand the
structural evolution of these isotopes, we carry a detailed calculation in a
definite symmetry-based framework, the interacting boson model with
configuration mixing (IBM-CM). We compare our calculation to a large range of
experimental data, such as energy levels, two neutron separation energies, $E2$
and $E0$ transition rates, isotope shifts and magnetic moments. The structural
evolution of the low lying spectra of these isotopes is explained using the
notion of intertwined quantum phase transitions (IQPTs), for which a QPT
involving a crossing of two configurations (Type II) is accompanied by a QPT
involving a shape evolution of each configuration separately (Type I). In our
study, we find the occurrence of Type I QPT within the intruder configuration,
changing from weakly deformed to prolate deformed and finally to
$\gamma$-unstable, associated with the U(5), SU(3) and SO(6) dynamical symmetry
limits of the IBM, respectively. Alongside the Type I QPT, we also find the
occurrence of Type II QPT between the normal and intruder configurations, where
both Types I and II have a critical-point near $A\approx100$. The good
agreement of our calculation with the vast empirical data along the chain of
isotopes demonstrates the relevance of IQPTs to the zirconium isotopes, and can
serve as a case study to set path for new investigations of IQPTs in other
nuclei and other physical systems.
