  Finite-temperature transport properties of one-dimensional systems can be
studied using the time dependent density matrix renormalization group via the
introduction of auxiliary degrees of freedom which purify the thermal
statistical operator. We demonstrate how the numerical effort of such
calculations is reduced when the physical time evolution is augmented by an
additional time evolution within the auxiliary Hilbert space. Specifically, we
explore a variety of integrable and non-integrable, gapless and gapped models
at temperatures ranging from T=infty down to T/bandwidth=0.05 and study both
(i) linear response where (heat and charge) transport coefficients are
determined by the current-current correlation function and (ii) non-equilibrium
driven by arbitrary large temperature gradients. The modified DMRG algorithm
removes an 'artificial' build-up of entanglement between the auxiliary and
physical degrees of freedom. Thus, longer time scales can be reached.
