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This paper provides a study and discussion of earlier as well as novel moreefficient schemes for the precise evaluation of finite-temperature responsefunctions of strongly correlated quantum systems in the framework of thetime-dependent density matrix renormalization group (tDMRG). The computationalcosts and bond dimensions as functions of time and temperature are examined forthe example of the spin-1/2 XXZ Heisenberg chain in the critical XY phase andthe gapped N\'eel phase. The matrix product state purifications occurring inthe algorithms are in one-to-one relation with corresponding matrix productoperators. This notational simplification elucidates implications ofquasi-locality on the computational costs. Based on the observation that thereis considerable freedom in designing efficient tDMRG schemes for thecalculation of dynamical correlators at finite temperatures, a new class ofoptimizable schemes, as recently suggested in arXiv:1212.3570, is explained andanalyzed numerically. A specific novel near-optimal scheme that requires noadditional optimization reaches maximum times that are typically increased by afactor of two, when compared against earlier approaches. These increasedreachable times make many more physical applications accessible. For each ofthe described tDMRG schemes, one can devise a corresponding transfer matrixrenormalization group (TMRG) variant.

Precise evaluation of thermal response functions by optimized density matrix renormalization group schemes