Laboratoire de Physique Théorique
Toulouse - UMR 5152

Disordered Heisenberg spin chains have been mostly studied by bosonization and real-space renormalization-group schemes. But the combined effects of disorder an frustration have not been extensively studied. The Majumdar-Ghosh model is a specific point of an antiferromagnetic chain with next-nearest-neighbour frustrated couplings. At this point, the ground state is exactly dimerized and elementary excitations can be described within a variationnal approach. We show that the effects of disorder on the Majumdar-Ghosh chain can be understood in terms of localization of deconfined spinons. For a specific choice of the disorder, the ground-state remains exactly dimerized and spinons obey to a 1D Anderson hamiltonian. Analytical results of the Anderson model are compared with DMRG simulations on the many-body system. When the disorder becomes strong enough, the gap is destroyed and the system enters a new phase. Without the specific choice of disorder, the gap vanishes for infinitely small disorder and the system can be studied by a decimation procedure.