Partial dynamical symmetry in quantum Hamiltonians with higher-order terms

TL;DR

This paper introduces a general method to build many-body quantum Hamiltonians with partial dynamical symmetry, enabling solvable states within complex interactions, demonstrated in nuclear models and applied to platinum-196.

Contribution

A new tensor decomposition approach to construct Hamiltonians with partial dynamical symmetry in many-body quantum systems.

Findings

Successfully applied to the SO(6) limit of the interacting boson model.

Constructed Hamiltonians with hierarchies of solvable states.

Validated method on the nucleus $^{196}$Pt.

Abstract

A generic procedure is proposed to construct many-body quantum Hamiltonians with partial dynamical symmetry. It is based on a tensor decomposition of the Hamiltonian and allows the construction of a hierarchy of interactions that have selected classes of solvable states. The method is illustrated in the SO(6) limit of the interacting boson model of atomic nuclei and applied to the nucleus $^{196}$Pt.