Autocorrelations from the transfer-matrix density-matrix renormalization-group method

Extending the transfer-matrix density-matrix renormalization-group algorithm, we are able to calculate imaginary time spin autocorrelations with high accuracy (absolute error $<{10}^{-6})$ over a wide temperature range $(0<\beta J<\mathrm{}20)$. After analytic continuation using the rules of probability theory along with the entropic prior (MaxEnt), we obtain real frequency spectra for the $\mathrm{XY}$ model, the isotropic Heisenberg, and the gapped Heisenberg-Ising model. Available exact results in some limits allow for a critical evaluation of the quality of answers expected from this procedure. We find that high-precision data are still insufficient for resolving specific line shapes such as low-frequency divergences. However, the method is appropriate for identifying low-temperature gaps and peak positions.