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For the simulation of equilibrium states and finite-temperature responsefunctions of strongly-correlated quantum many-body systems, we compare theefficiencies of two different approaches in the framework of the density matrixrenormalization group (DMRG). The first is based on matrix productpurifications. The second, more recent one, is based on so-called minimallyentangled typical thermal states (METTS). For the latter, we highlight theinterplay of statistical and DMRG truncation errors, discuss the use ofself-averaging effects, and describe schemes for the computation of responsefunctions. For critical as well as gapped phases of the spin-1/2 XXZ chain andthe one-dimensional Bose-Hubbard model, we assess the computation costs andaccuracies of the two methods at different temperatures. For almost allconsidered cases, we find that, for the same computation cost, purificationsyield more accurate results than METTS -- often by orders of magnitude. TheMETTS algorithm becomes more efficient only for temperatures well below thesystem's energy gap. The exponential growth of the computation cost in theevaluation of response functions limits the attainable timescales in bothmethods and we find that in this regard, METTS do not outperform purifications.

Minimally entangled typical thermal states versus matrix product purifications for the simulation of equilibrium states and time evolution