2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/105482We introduce and motivate the study of quantum spin chains on a one-dimensional lattice. We classify the varieties of methods that have been used to study these models into three categories, - a) exact methods to study specific models b) field theories to describe fluctuations about the classical ordered phases and c) numerical methods. We then discuss the $J_1$-$J_2$-$δ$ model in some detail and end with a few comments on open problems.8 pages, Proceedings of CMDAYS05, Berhampur, to be published in Indian Jnl of PhysicsStatistical MechanicsStrongly Correlated Electronstext