Textures as a phase-transition probe for quantum spin chains

The idea of quantum texture has been recently proposed and used as a tool for quantifying coherences and for quantum gate identification. In this work we offer a study on its usage to quantum phase transitions, demonstrating the rugosity metric as a simple tool for effective phase-transition probing. We establish the link between rugosity in the computational basis and the hierarchy of spin correlators, and analyze rugosities defined in the global ground-state and in ground-states belonging to different magnetization sectors (to which we refer to as global vs symmetry-resolved rugosities) to study the phase diagram of the Heisenberg XXZ model. We find distinct rugosity signatures at both transition points. In particular, a sharp feature appears at Δ=1 already for small systems, revealing a pronounced sensitivity of the correlation hierarchy encoded by the texture to this point. Since the BKT transition coincides with the isotropic SU(2) point of the XXZ model, this behavior may reflect a particular sensitivity of rugosity to the structure of the spin-correlation hierarchy at isotropy.