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In the past decades, topological concepts have emerged to classify matterstates beyond the Ginzburg-Landau symmetry breaking paradigm. The underlyingglobal invariants are usually characterized by integers, such as Chern orwinding numbers. Very recently, band topology characterized by non-Abeliantopological charges has been proposed, which possess non-commutative andfruitful 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 beenreported. Here, we experimentally observe the non-Abelian topological chargesin a PT (parity and time-reversal) symmetric system. More importantly, wepropose non-Abelian bulk-edge correspondence, where edge states are found to bedescribed by non-Abelian charges. Our work opens the door towards non-Abeliantopological phase characterization and manipulation.

Experimental observation of non-Abelian topological charges and bulk-edge correspondence