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

TL;DR

This paper explores topological phases in quasi-periodic spin chains using numerical and K-theoretic methods, revealing non-commutative tori operator algebras and robust edge modes with potential for topological spin pumping.

Contribution

It demonstrates the non-commutative torus structure of Hamiltonian algebras in quasi-periodic chains and introduces a framework for topological spin pumping via phason adiabatic cycles.

Findings

Operator algebras are non-commutative tori.

Edge modes are hybrid and influenced by interactions.

Framework for topological spin pumping is established.

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.