We improve a recently developed expansion technique for calculating real
frequency spectral functions of any one-dimensional model with short-range
interactions, by postprocessing computed Chebyshev moments with linear
prediction. This can be achieved at virtually no cost and, in sharp contrast to
existing methods based on the dampening of the moments, improves the spectral
resolution rather than lowering it. We validate the method for the exactly
solvable resonating level model and the single impurity Anderson model. It is
capable of resolving sharp Kondo resonances, as well as peaks within the
Hubbard bands when employed as an impurity solver for dynamical mean-field
theory (DMFT). Our method works at zero temperature and allows for arbitrary
discretization of the bath spectrum. It achieves similar precision as the
dynamical density matrix renormalization group (DDMRG), at lower cost. We also
propose an alternative expansion, of 1-exp(-tau H) instead of the usual H,
which opens the possibility of using established methods for the time evolution
of matrix product states to calculate spectral functions directly.Comment: 13 pages, 9 figure
