Quantum magnets: a brief overview

Quantum magnetism is one of the most active areas of research in condensed matter physics. There is significant research interest specially in low-dimensional quantum spin systems. Such systems have a large number of experimental realizations and exhibit a variety of phenomena the origin of which can be attributed to quantum effects and low dimensions. In this review, an overview of some aspects of quantum magnetism in low dimensions is given. The emphasis is on key concepts, theorems and rigorous results as well as models of spin chains, ladders and frustated magnetic systems.