2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/95474A relation between geometric phases and criticality of spin chains is established. As a result, we show how geometric phases can be exploited as a tool to detect regions of criticality without having to undergo a quantum phase transition. We analytically evaluate the geometric phase that correspond to the ground and excited states of the anisotropic XY model in the presence of a transverse magnetic field when the direction of the anisotropy is adiabatically rotated. Ultra-cold atoms in optical lattices are presented as a possible physical realization.4 pages, 1 figures, RevTeX Analysis of resilience against errors and generalizations addedMesoscale and Nanoscale PhysicsQuantum Physicstext