# Intertwined quantum phase transitions in the Zr chain

## TL;DR

This paper introduces the concept of intertwined quantum phase transitions (IQPTs) and provides evidence for their occurrence in Zr isotopes, where two configurations cross and evolve shape simultaneously, revealing complex nuclear shape dynamics.

## Contribution

The paper defines IQPTs and demonstrates their presence in Zr isotopes using the interacting boson model with configuration mixing, highlighting a novel type of quantum phase transition.

## Key findings

- Identification of IQPTs in Zr isotopes.
- Normal configuration remains spherical while the intruder configuration undergoes shape transitions.
- Evidence of shape coexistence and complex evolution in nuclear configurations.

## Abstract

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 in the 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)$\to$SU(3)] QPT and then a crossover to $\gamma$-unstable [SU(3)$\to$SO(6)].