  We show from the symmetries of the many body Hamiltonian, cast into the form
of the Heisenberg (spin) Hamiltonian, that the fractional periodicities of
persistent currents are due to the breakdown of internal symmetry and the spin
Hamiltonian holds the explanation to this transition. Numerical
diagonalizations are performed to show this explicitely. Persistent currents
therefore, provide an easy way to experimentally verify broken internal
symmetry in electronic systems.
