Partial Dynamical Symmetry in a Fermionic Many-body System

The fundamental concept underlying algebraic theories in quantum physics is that of an exact or dynamical symmetry. Realistic quantum systems, however, often require the associated symmetry to be broken in order to allow for a proper description of some observed basic features. Partial dynamical symmetry (PDS) describes an intermediate situation in which some eigenstates exhibit a symmetry which the associated Hamiltonian does not share. The objective of this approach is to remove undesired constraints from the theory while preserving the useful aspects of a dynamical symmetry, such as solvability, for a subset of eigenstates. Here we present an example of a PDS in an interacting fermion system. In the symplectic shell model of nuclei, we introduce PDS Hamiltonians which are closely related to the nuclear quadrupole-quadrupole interaction. An application to C is discussed.