Exotic Non-Abelian Topological Defects in Lattice Fractional Quantum Hall States

Abstract

We investigate extrinsic wormholelike twist defects that effectively increase the genus of space in lattice versions of multicomponent fractional quantum Hall systems. Although the original band structure is distorted by these defects, leading to localized midgap states, we find that a new lowest flat band representing a higher genus system can be engineered by tuning local single-particle potentials. Remarkably, once local many-body interactions in this new band are switched on, we identify various Abelian and non-Abelian fractional quantum Hall states, whose ground-state degeneracy increases with the number of defects, i.e, with the genus of space. This sensitivity of topological degeneracy to defects provides a "proof of concept" demonstration that genons, predicted by topological field theory as exotic non-Abelian defects tied to a varying topology of space, do exist in realistic microscopic models. Specifically, our results indicate that genons could be created in the laboratory by combining the physics of artificial gauge fields in cold atom systems with already existing holographic beam shaping methods for creating twist defects.

10 pages, 11 figures, including a Supplementary Material. Published version

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Cited by in corpus (10)

• The boundaries and twist defects of the color code and their applications to topological quantum computation
• Stability of fractional Chern insulators in the effective continuum limit of Harper-Hofstadter bands with Chern number $|C|>1$
• Stability, phase transitions, and numerical breakdown of fractional Chern insulators in higher Chern bands of the Hofstadter model
• Recent Developments in Fractional Chern Insulators
• Characterization of quasiholes in two-component fractional quantum Hall states and fractional Chern insulators in $|C|=2$ flat bands
• Numerical investigation of gapped edge states in fractional quantum Hall-superconductor heterostructures
• A dark state of Chern bands: Designing flat bands with higher Chern number
• Intertwined Order in Fractional Chern Insulators from Finite-Momentum Pairing of Composite Fermions
• Fractional quantum Hall states with gapped boundaries in an extreme lattice limit
• The Kitaev honeycomb model on surfaces of genus $g\ge 2$