Topological Gaps in Quasi-Periodic Spin Chains: A Numerical and K-Theoretic Analysis

Abstract

Topological phases supported by quasi-periodic spin-chain models and their bulk-boundary principles are investigated by numerical and K-theoretic methods. We show that, for both the un-correlated and correlated phases, the operator algebras that generate the Hamiltonians are non-commutative tori, hence the quasi-periodic chains display physics akin to the quantum Hall effect in two and higher dimensions. The robust topological edge modes are found to be strongly shaped by the interaction and, generically, they have hybrid edge-localized and chain-delocalized structures. Our findings lay the foundations for topological spin pumping using the phason of a quasi-periodic pattern as an adiabatic parameter, where selectively chosen quantized bits of magnetization can be transferred from one edge of the chain to the other.

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• Physical properties of an Aperiodic monotile: Graphene-like features, chirality and zero-modes
• A groupoid approach to interacting fermions
• Topology in quasicrystals
• Mapping Chern numbers in quasi-periodic interacting spin chains
• Cyclic cocycles and quantized pairings in materials science
• A $C^{\ast }$-algebraic view on the interaction of real- and reciprocal space topology in skyrmion crystals