  We analyze the thermal conductivity of anisotropic and frustrated spin-1/2
chains using analytical and numerical techniques. This includes mean-field
theory based on the Jordan-Wigner transformation, bosonization, and exact
diagonalization of systems with N<=18 sites. We present results for the
temperature dependence of the zero-frequency weight of the conductivity for
several values of the anisotropy \Delta. In the gapless regime, we show that
the mean-field theory compares well to known results and that the
low-temperature limit is correctly described by bosonization. In the
antiferromagnetic and ferromagnetic gapped regime, we analyze the temperature
dependence of the thermal conductivity numerically. The convergence of the
finite-size data is remarkably good in the ferromagnetic case. Finally, we
apply our numerical method and mean-field theory to the frustrated chain where
we find a good agreement of these two approaches on finite systems. Our
numerical data do not yield evidence for a diverging thermal conductivity in
the thermodynamic limit in case of the antiferromagnetic gapped regime of the
frustrated chain.
