2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/126719In this work, we show that the quantum compass model on an square lattice can be mapped to a fermionic model with local density interaction. We introduce a mean-field approximation where the most important fluctuations, those perpendicular to the ordering direction, are taken into account exactly. It is found that the quantum phase transition point at $J_x=J_z$ marks a first order phase transition. We also show that the mean field result is robust against the remaining fluctuation corrections up to the second order.7 pages, 10 figsStrongly Correlated Electronstext