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.
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