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

Abstract

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.

20 pages, 4 figures

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• Non-Abelian lattice gauge fields in the photonic synthetic frequency dimension
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• Floquet multi-gap topology: Non-Abelian braiding and anomalous Dirac string phase
• Non-Abelian effects in dissipative photonic topological lattices
• Minimal non-abelian nodal braiding in ideal metamaterials
• Artificial non-Abelian lattice gauge fields for photons in the synthetic frequency dimension
• Experimental observation of non-Abelian earring nodal links in phononic crystals
• Homotopy, Symmetry, and Non-Hermitian Band Topology
• Observation of topological Euler insulators with a trapped-ion quantum simulator
• Synthetic non-Abelian gauge fields for non-Hermitian systems
• Quantized Integrated Shift Effect in Multigap Topological Phases
• Optical manifestations and bounds of topological Euler class
• Non-Abelian charged nodal links in dielectric photonic crystal
• Floquet Non-Abelian Topological Insulator and Multifold Bulk-Edge Correspondence
• Non-Abelian Generalizations of the Hofstadter model: Spin-orbit-coupled Butterfly Pairs
• Topological continuum charges of acoustic phonons in 2D
• Non-Abelian Hopf-Euler insulators
• Observation of flat-band and band transition in the synthetic space
• Quantum Valley Hall effect without Berry curvature
• Unsupervised Learning of Topological Non-Abelian Braiding in Non-Hermitian Bands
• Non-Hermitian non-Abelian topological insulators with $PT$ symmetry
• Three-dimensional $\mathcal{P}\mathcal{T}$-symmetric topological phases with Pontryagin index
• Interferometry of non-Abelian band singularities and Euler class topology
• Observation of squeezed Chern insulator in an acoustic fractal lattice
• Experimental demonstration of non-adjacent band topology connecting multiple nodal links
• Disorder-induced topological quantum phase transitions in multi-gap Euler semimetals
• Photonic nodal lines with quadrupole Berry curvature distribution
• Triple nodal points characterized by their nodal-line structure in all magnetic space groups
• Demonstration of non-Abelian frame charge flow in photonic crystals
• Hermitian Topologies originating from non-Hermitian braidings
• Direct measurement of topological invariants through temporal adiabatic evolution of bulk states in the synthetic Brillouin zone
• Exact projected entangled pair ground states with topological Euler invariant
• Synthetic non-Abelian topological charges in ultracold atomic gases
• Andreev reflection in Euler materials
• Braiding topology of symmetry-protected degeneracy points in non-Hermitian systems
• Observing the nodal-line conversion determined by the relative homotopy
• Implementing non-Abelian Hatano-Nelson model in electric circuits
• All hourglass bosonic excitations in the 1651 magnetic space groups and 528 magnetic layer groups
• Topological Singularities in Metasurface Scattering Matrices: From Nodal Lines to Exceptional Lines
• Coexisting Euler and Stiefel-Whitney Topological Phases in Elastic Metamaterials
• Observation of edge solitons and transitions between them in a trimer circuit lattice
• Second Euler number in four dimensional synthetic matter
• Floquet non-Abelian topological charges and edge states
• N-Band Photonic Hopf Insulators Based on 2D Microring Lattices
• From quantum geometry to non-linear optics and gerbes: Recent advances in topological band theory
• Tensor Theory for Higher Dimensional Chern Insulators with Large Chern Numbers
• Breakdown of boundary criticality and exotic topological semimetals in $\mathcal{P}\mathcal{T}$-invariant systems
• High-chirality and multiquaternion Weyl nodes in hexagonal ReO${}_3$
• Euler band topology in superfluids and superconductors
• Non-Abelian interference of topological edge states
• Coupled-wire construction of non-Abelian higher-order topological phases
• Three-dimensional spinless Euler insulators with rotational symmetry
• Asymmetric real topology of conduction and valence bands
• Gapped spinful phases obtained via Gutzwiller projections of Euler states
• Orbital magnetization reveals multiband topology
• Hinge modes of three-dimensional Euler insulators
• Semimetals without correspondence between the topological charge of nodal line/surface and Fermi arc