Microscopic analysis of nuclear quantum phase transitions in the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi mathvariant="bold-italic">N</mml:mi><mml:mo>≈</mml:mo><mml:mn>90</mml:mn></mml:mrow></mml:math>region

The analysis of shape transitions in Nd isotopes, based on the framework of relativistic energy-density functionals and restricted to axially symmetric shapes in T. Nik\ifmmode \check{s}\else \v{s}\fi{}i\ifmmode \acute{c}\else \'{c}\fi{}, D. Vretenar, G. A. Lalazissis, and P. Ring [Phys. Rev. Lett. 99, 092502 (2007)], is extended to the region $Z=60,62,64$ with $N\ensuremath{\approx}90$ and includes both $\ensuremath{\beta}$ and $\ensuremath{\gamma}$ deformations. Collective excitation spectra and transition probabilities are calculated starting from a five-dimensional Hamiltonian for quadrupole vibrational and rotational degrees of freedom, with parameters determined by constrained self-consistent relativistic mean-field calculations for triaxial shapes. The results reproduce available data and show that there is an abrupt change of structure at $N=90$ that can be approximately characterized by the X(5) analytic solution at the critical point of the first-order quantum phase transition between spherical and axially deformed shapes.