We illustrate how finite-temperature charge and thermal Drude weights of one-
dimensional systems can be obtained from the relaxation of initial states
featuring global (left–right) gradients in the chemical potential or
temperature. The approach is tested for spinless interacting fermions as well
as for the Fermi-Hubbard model, and the behavior in the vicinity of special
points (such as half filling or isotropic chains) is discussed.We present
technical details on how to implement the calculation in practice using the
density matrix renormalization group and show that the non-equilibrium
dynamics is often less demanding to simulate numerically and features simpler
finite-time transients than the corresponding linear response current
correlators; thus, new parameter regimes can become accessible. As an
application, we determine the thermal Drude weight of the Hubbard model for
temperatures T which are an order of magnitude smaller than those reached in
the equilibrium approach. This allows us to demonstrate that at low T and half
filling, thermal transport is successively governed by spin excitations and
described quantitatively by the Bethe ansatz Drude weight of the Heisenberg
chain
