We present time-dependent density matrix renormalization group simulations (t-DMRG) at finite temperatures. It is demonstrated how a combination of finite-temperature t-DMRG and time-series prediction allows for an easy and very accurate calculation of spectral functions in one-dimensional quantum systems, irrespective of their statistics for arbitrary temperatures. This is illustrated with spin structure factors of $XX$ and $XXX$ spin-1/2 chains. For the $XX$ model we can compare against an exact solution, and for the $XXX$ model (Heisenberg antiferromagnet) against a Bethe ansatz solution and quantum Monte Carlo data.
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Barthel et al. (2009) studied this question.