One-dimensional quantum spin systems. Disorder and impurities.

Summary This thesis gathers three works which concern respectively the disordered spin chain 1, the non-magnetic impurities in the spin chain 1/2 and the reaction-diffusion processes. The weakly disordered spin chain 1 is studied by the abelian bosonization and the renormalization group. This technique allows to take into account the competition between disorder and interactions, and predicts the fate of the different phases of the anisotropic spin chain 1 under several types of disorder. One result is the high stability of the Haldane phase, and the instability of the antiferromagnetic phase under random magnetic field, which are proved by renormalization group arguments. A second work uses non-magnetic impurities as local probes of correlations in the 1/2 spin chain. In the case where the impurities are coupled to the edge of the chain, I predict a radically different temperature behavior of the nuclear spin relaxation rate of the impurities (11T,) than in the case where the same impurities are coupled to the entire chain. This can in particular be used to measure the surface exponents of one-dimensional quantum systems. The last work deals with one-dimensional reaction-diffusion processes whose transfer matrix is expressed as a spin model. The Jordan-Wigner transformation is used to obtain a fermionic field theory whose critical exponents are deduced from the renormalization group. This new approach provides an alternative method to the c-developments, and seems to be validated by the reasonable agreement with numerical results for the de Schlôgl reaction.