Topological Phenomena Protected by Diabolical Textures

Abstract

We present a new class of topological phenomena in inhomogeneous systems arising from the adiabatic spatial embedding of parametrized families of quantum states such as charge pumps and their generalizations. We demonstrate that each topologically distinct class of these ``diabolical textures" gives rise to distinct gapped states that are separated by ``trap-scaling" critical points, defect transitions, or intervening phases. Their phase diagrams exhibit versions of ``unnecessary criticality'' and ``multiversality,'' within a noninteracting setting. We demonstrate this in a one-dimensional Thouless pump texture trapping a charge and a two-dimensional class D texture trapping a Kitaev chain, including an analysis of their stability under weak symmetry-preserving perturbations and interactions. For systems in arbitrary spatial dimensions and global symmetries, we present a framework to systematically classify diabolical textures using Kitaev's $\Omega$ spectrum conjecture.

arXiv comment32 pages, 11 figures (main text + end matter + supplemental materials). v2: Added 2d example, introduced end matter, expanded supplemental materials