Anisotropy lifts topological protection of transport in pumped spin chains

arXiv:2611.08385

Mainak Pal

We investigate the prospect of topological spin pumping and transport in a dimerized spin-$\frac{1}{2}$ anisotropic XY chain with tunable in-plane anisotropy. Through a Jordan-Wigner transformation, the system maps onto an extended Rice-Mele-type fermionic model whose momentum-space band structure exhibits gapped regions characterized by nonzero Chern numbers ($\pm 1$) as well as trivial and gapless regimes. Conventional momentum-space analysis therefore predicts quantized Thouless-type spin pumping in parts of the Chern number diagram. However, real-space time evolution under open boundary conditions reveals that the spin transport is generally not quantized away from the isotropic limit. In the anisotropic regime, eigen-energy states within the transporting subspace hybridize during the driving cycle, leading to a transport that depends on details of the driving protocol. Quantized pumping and transport survive only in the isotropic limit, where the Hamiltonian reduces to decoupled Rice-Mele sectors and the transported spin component is conserved. Our results demonstrate that momentum-space topological invariants alone do not guarantee quantized spin transport in anisotropic spin chains. More broadly, they show that the conventional Thouless-pumping framework does not straightforwardly extend to situations where the transported quantity is not conserved, highlighting the importance of real-space diagnostics in topological transport phenomena.