Transport properties of integrable quantum systems

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Some of the most dramatic consequences of the interplay of reduced dimensionality and quantum effects are observed in transport. Integrable models, which have an infinite 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 infinite heat conductance. The spin current operator, on the other hand, is not conserved, but is known to have a finite overlap with conserved charges leading to a nonzero spin Drude weight at finite temperatures. So far, however, a Mazur bound for the spin Drude weight based on these charges has only been obtained at infinite temperatures.The aim of this project is twofold: (a) We will algebraically construct quasi-local charges which have a nonzero overlap with the spin current operator and evaluate the corresponding Mazur bound for all temperatures. The results of these investigations are also expected to be highly relevant for quench dynamics in integrable models. (b) We will calculate the full Drude weight based on functional equations for the energy level curvatures within a fusion algebra approach. This approach avoids the conceptual and technical issues of previous calculations based on the thermodynamic Bethe ansatz (TBA) and will show whether or not the TBA results are valid. Our analytical results will be checked against numerical data obtained using time-dependent DMRG algorithms.