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Intertwined quantum phase transitions in the Zr isotopes

We explore the situation of intertwined quantum phase transitions (IQPTs), for which a QPT involving a crossing of two configurations is accompanied by a shape evolution of each configuration with its own separate QPT. We demonstrate the relevance of IQPTs to the Zr isotopes, with such coexisting Type I and Type II QPTs, and ground state shapes changing from spherical to prolate axially deformed and finally to gamma-unstable. Evidence for this scenario is provided by a detailed comparison with experimental data, using a definite symmetry-based conceptual framework.