  Ring exchange is an elementary interaction for modeling unconventional
topological matters which hold promise for efficient quantum information
processing. We report the observation of four-body ring-exchange interactions
and the topological properties of anyonic excitations within an ultracold atom
system. A minimum toric code Hamiltonian in which the ring exchange is the
dominant term, was implemented by engineering a Hubbard Hamiltonian that
describes atomic spins in disconnected plaquette arrays formed by two
orthogonal superlattices. The ring-exchange interactions were resolved from the
dynamical evolutions in the spin orders, matching well with the predicted
energy gaps between two anyonic excitations of the spin system. A braiding
operation was applied to the spins in the plaquettes and an induced phase
$1.00(3)\pi$ in the four-spin state was observed, confirming
$\frac{1}{2}$-anynoic statistics. This work represents an essential step
towards studying topological matters with many-body systems and the
applications in quantum computation and simulation.
