# Intertwined Quantum Phase Transitions in the Zr Isotopes

## TL;DR

This paper investigates intertwined quantum phase transitions in Zr isotopes, revealing complex shape evolutions and configuration crossings, supported by experimental data and symmetry-based analysis.

## Contribution

It introduces the concept of intertwined quantum phase transitions and demonstrates their relevance to Zr isotopes with coexisting shape transitions.

## Key findings

- Identification of coexisting Type I and Type II QPTs in Zr isotopes
- Ground state shapes evolve from spherical to deformed to gamma-unstable
- Strong agreement between theoretical analysis and experimental data

## Abstract

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.