  We experimentally realize a Peierls phase in the hopping amplitude of
excitations carried by Rydberg atoms, and observe the resulting characteristic
chiral motion in a minimal setup of three sites. Our demonstration relies on
the intrinsic spin-orbit coupling of the dipolar exchange interaction combined
with time-reversal symmetry breaking by a homogeneous external magnetic field.
Remarkably, the phase of the hopping amplitude between two sites strongly
depends on the occupancy of the third site, thus leading to a correlated
hopping associated to a density-dependent Peierls phase. We experimentally
observe this density-dependent hopping and show that the excitations behave as
anyonic particles with a non-trivial phase under exchange. Finally, we confirm
the dependence of the Peierls phase on the geometrical arrangement of the
Rydberg atoms.
