Intertwined quantum phase transitions in the Zr chain

We introduce the notion of intertwined quantum phase transitions (IQPTs), for which a crossing of two configurations coexists with a pronounced shape-evolution of each configuration. A detailed analysis in the framework of the interacting boson model with configuration mixing, provides evidence for this scenario inthe Zr isotopes. The latter exhibit a normal configuration which remains spherical along the chain, but exchanges roles with an intruder configuration, which undergoes first a spherical to prolate-deformed [U(5)→SU(3)] QPT and then a crossover to γ-unstable [SU(3)→SO(6)].