Quantum mechanics

Theoretical physics

Pure mathematics

Topological quantum number

Topological degeneracy

Abelian group

Symmetry protected topological order

Physics

Topological order

Mathematics

Invariant (physics)

Parity (physics)

Quantum

Combinatorics

Topological entropy in physics

Topology (electrical circuits)

Nature

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.

Experimental observation of non-Abelian topological charges and edge states