An algebraic approach to intertwined quantum phase transitions in the Zr isotopes

The algebraic framework of the interacting boson model with configuration mixing is employed to demonstrate the occurrence of intertwined quantum phase transitions (IQPTs) in the ${}_{40}$Zr isotopes with neutron number 52-70. The detailed quantum and classical analyses reveal a QPT of crossing normal and intruder configurations superimposed on a QPT of the intruder configuration from U(5) to SU(3) and a crossover from SU(3) to SO(6) dynamical symmetries.