Quantum Antiferromagnetism : A theoretical and numerical investigation of low dimensional strongly correlated fermionic systems

Although its long history, the mystery of ferromagnetism was revealed in the last century only, with the birth of quantum mechanics and the introduction of the spin. Besides the phenomena of magnetic ordering, strong correlations in condensed matter systems have other spectacular consequences, high temperature superconductivity above all. The theory of the origin of magnetic interactions remains one of the less developed areas of solid state physics, where large efforts, both in experiments and theory, concentrate. This book is mainly devoted to the investigation of two low-dimensional spin systems with spin-lattice coupling. In the former part, we focus on the role of coupling between spins and adiabatic phonons and of competitive interactions in stabilizing magnetization plateaus in antiferromagnetic Heisenberg models on square lattice. In the second part of the dissertation our attention moves to antiferromagnetic molecular rings, where a microscopic theory of magnetoelastic coupling is developed in order to interpret some unconventional features in experimental measurements.