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  • In the critical regime |Δ| < 1, spin transport in the integrable spin-1/2 XXZ Heisenberg chain is ballistic at finite temperature, characterised by a finite spin Drude weight. This thesis studies the spin Drude weight with exact methods based on integrability, following two complementary approaches.The first approach is based on the Mazur inequality. Since local conserved charges do not contribute at zero magnetic field, we use quasi-local charges and formulate the resulting Mazur bound at finite temperature within the quantum transfer matrix approach, in terms of non-linear integral equations (NLIEs) derived from T- and Y-system functional relations. In the high-temperature limit, the known result is recovered.The second approach evaluates the finite-temperature Kohn formula, which expresses the Drude weight through the curvatures of the energy levels with respect to a magnetic flux. Using the row-to-row transfer matrix, the curvatures are expressed through Y-functions and their zeros, avoiding the string hypothesis. We derive NLIEs for simple roots of unity and for the case ν = 5/2, and show numerically that the approach reproduces Zotos' formula. The Drude weight depends strongly on the system size and converges very slowly to the thermodynamic limit.
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