  Many fundamental one-dimensional lattice models such as the Heisenberg or the
Hubbard model are integrable. For these microscopic models, parameters in the
Luttinger liquid theory can often be fixed and parameter-free results at low
energies for many physical quantities such as dynamical correlation functions
obtained where exact results are still out of reach. Quantum integrable models
thus provide an important testing ground for low-energy Luttinger liquid
physics. They are, furthermore, also very interesting in their own right and
show, for example, peculiar transport and thermalization properties. The
consequences of the conservation laws leading to integrability for the
structure of the low-energy effective theory have, however, not fully been
explored yet. I will discuss the connection between integrability and Luttinger
liquid theory here, using the anisotropic Heisenberg model as an example. In
particular, I will review the methods which allow to fix free parameters in the
Luttinger model with the help of the Bethe ansatz solution. As applications,
parameter-free results for the susceptibility in the presence of non-magnetic
impurities, for spin transport, and for the spin-lattice relaxation rate are
discussed.
