Partial Dynamical Symmetries

TL;DR

This paper reviews partial dynamical symmetry (PDS), highlighting algorithms to identify Hamiltonians with PDS, and discusses their applications in nuclear spectroscopy, quantum phase transitions, and mixed dynamical systems.

Contribution

It introduces general algorithms for identifying interactions with partial dynamical symmetry and constructs explicit Hamiltonians exhibiting PDS in bosonic and fermionic models.

Findings

PDS is relevant to nuclear spectroscopy.

PDS plays a role in quantum phase transitions.

PDS is applicable to systems with mixed dynamics.

Abstract

This overview focuses on the notion of partial dynamical symmetry (PDS), for which a prescribed symmetry is obeyed by a subset of solvable eigenstates, but is not shared by the Hamiltonian. General algorithms are presented to identify interactions, of a given order, with such intermediate-symmetry structure. Explicit bosonic and fermionic Hamiltonians with PDS are constructed in the framework of models based on spectrum generating algebras. PDSs of various types are shown to be relevant to nuclear spectroscopy, quantum phase transitions and systems with mixed chaotic and regular dynamics.