  In the past decades, topological concepts have emerged to classify matter
states beyond the Ginzburg-Landau symmetry breaking paradigm. The underlying
global invariants are usually characterized by integers, such as Chern or
winding numbers. Very recently, band topology characterized by non-Abelian
topological charges has been proposed, which possess non-commutative and
fruitful braiding structures with multiple (>1) bandgaps entangled together.
Despite many potential exquisite applications including quantum computations,
no experimental observation of non-Abelian topological charges has been
reported. Here, we experimentally observe the non-Abelian topological charges
in a PT (parity and time-reversal) symmetric system. More importantly, we
propose non-Abelian bulk-edge correspondence, where edge states are found to be
described by non-Abelian charges. Our work opens the door towards non-Abelian
topological phase characterization and manipulation.
