Impurities and disorder in nearly integrable models

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The effects of impurities in spin-1/2 Heisenberg chains are recently experiencing a renewed interest due to experimental realizations in solid state systems and ultra-cold gases. Due to spatial confinement impurities have strong impact on the magnetic excitation spectrum and transport properties in one dimension. Already the smallest generic scatterer can block the magnetic conductance which leads to effectively isolated finite chain segments with discrete energies and characteristic boundary correlations. Surprisingly, relatively little is known about impurity effects on the momentum- and frequency resolved dynamical structure factor. A simple model based on finite chain segments predicts a pseudogap in the weak disorder limit. This must be contrasted to the strong disorder limit modelled by the random bond spin chain where a divergent low energy dynamical structure factor is predicted. Now it would be important to account for experimentally relevant thermal fluctuations, next-nearest neighbour spin couplings and magnetic properties of the impurities. In this project we aim for a full understanding of the effects of impurities on the dynamical structure factor of one-dimensional spin chains. Bonds linking the finite chain segments, other type of impurities and finite temperature will be taken into account. Eventually we will increase the disorder concentration and investigate the crossover from weak disorder to the strong disorder random singlet phase.