2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/20702We study magnetic order in the Heisenberg antiferromagnet on the checkerboard lattice, a two-dimensional version of the pyrochlore network with strong geometric frustration. By employing the semiclassical (1/S) expansion we find that quantum fluctuations of spins induce a long-range order that breaks the four-fold rotational symmetry of the lattice. The ordered phase is a valence-bond crystal. We discuss similarities and differences with the extreme quantum case S = 1/2 and find a useful phenomenology to describe the bond-ordered phases.Minor clarifications + reference to an informal introduction cond-mat/0308091Strongly Correlated Electronstext