Some of the most dramatic consequences of the interplay of reduced dimensionality and
quantum e ects are observed in transport. Integrable models, which have an in finite number
of local conservation laws, are expected to have particularly unusual transport properties.
For the integrable spin-1/2 Heisenberg chain the energy current itself is conserved
leading to an in finite heat conductance. The spin current operator, on the other hand, is
not conserved, but is known to have a fi nite overlap with conserved charges leading to a
nonzero spin Drude weight at fi nite temperatures. So far, however, a Mazur bound for the
spin Drude weight based on these charges has only been obtained at infi nite temperatures.
The aim of this project is to extend these calculations to all temperatures and to obtain the full Drude weight based on functional equations for the energy level curvatures.