Hidden Euclidean dynamical symmetry in the U(n+1) vibron model

TL;DR

This paper reveals a hidden Euclidean dynamical symmetry in the U(n+1) vibron model at the quantum phase transition point, supported by theoretical analysis and experimental data from $^{82}$Kr.

Contribution

It demonstrates the emergence of E(n) dynamical symmetry at the critical point of the U(n)-SO(n+1) phase transition in the vibron model, linking theory with experimental observations.

Findings

E(n) symmetry emerges at the critical point.

Low-lying structure of $^{82}$Kr exemplifies E(5) symmetry.

Theoretical analysis confirms the symmetry's role in phase transition.

Abstract

Based on the boson realization of the Euclidean algebras, it is found that the E($n$) dynamical symmetry (DS) may emerge at the critical point of the U($n$)-SO($n+1$) quantum phase transition. To justify this finding, we provide a detailed analysis of the critical dynamics in the U($n+1$) vibron model in both quantal and classical ways. It is further shown that the low-lying structure of $^{82}$Kr may serve as an excellent empirical realization of the E(5) DS in experiments.