Simulations of pure and doped low-dimensional spin-1/2 gapped systems

Low dimensional spin-1/2 systems with antiferromagnetic interactions display very innovative features, driven by strong quantum fluctuations. In particular, geometrical effects or competing magnetic interactions can give rise to the formation of a spin gap between the singlet ground state and the first excited triplet state. In this chapter, we focus on the numerical investigation of such systems by Exact Diagonalisation methods and some extensions of it including a simultaneous mean-field treatment of some perturbative couplings. After a presentation of the Lanczos algorithm and a description of the space group symmetries, we give a short review on some pure low-dimensionnal frustrated spin gapped systems. In particular, we outline the role of the magnetic frustration in the formation of disordered phase. A large part is also devoted to frustrated Spin-Peierls systems for which the role of interchain couplings as well as impurity doping effects has been studied numerically.