Why did the Battle of Rancagua end the period called la patria vieja?

The Battle of Rancagua, which took place on October 1 and 2, 1814, marked the end of the period known as la patria vieja ("the old fatherland") because it allowed Spain to reestablish its military supremacy over the colony.12

During this engagement, Spanish royalist forces defeated the republican troops led by Bernardo O’Higgins, effectively crushing the initial independence movement that had begun in 1810. Following this decisive defeat, key patriot leaders—including O’Higgins and the Carrera brothers—were forced to flee to [Argentina]. This migration set the stage for the later liberation efforts led by José de San Martín, which eventually resumed the struggle for Chilean independence with the Battle of Chacabuco in 1817.1324