Youcef Mohdeb

• In this thesis, we discuss the properties of quantum antiferromagnetic spin chains with long-range (LR) tunable interactions and positional disorder. By long-range, we mean that the range of interactions falls-off as a power law with the distance. We mainly focus on the entanglement properties of these systems and consider both ground state and high-energy eigenstates. Additionally, the dynamical properties of the LR random spin chain are considered by investigating the post-quench entanglement growth as a function of time. Finally, we study the response of this system to a local perturbation by considering the quantum fidelity variations with system size. While analytical results for LR interacting disordered systems are not abundant in the literature, we achieve the implementation of strong disorder renormalization group(SDRG) procedures (and variants) on such models. We systematically confront our results with numerical exact diagonalization(ED) to confirm the obtained predictions.