Spectral functions and time evolution from the Chebyshev recursion

We link linear prediction of Chebyshev and Fourier expansions to analytic continuation. We push the resolution in the Chebyshev-based computation of T=0 many-body spectral functions to a much higher precision by deriving a modified Chebyshev series expansion that allows to reduce the expansion order by a factor ∼16. We show that in a certain limit the Chebyshev technique becomes equivalent to computing spectral functions via time evolution and subsequent Fourier transform. This introduces a novel recursive time evolution algorithm that instead of the group operator e−iHt only involves the action of the generator H. For quantum impurity problems, we introduce an adapted discretization scheme for the bath spectral function. We discuss the relevance of these results for matrix product state (MPS) based DMRG-type algorithms, and their use within dynamical mean-field theory (DMFT). We present strong evidence that the Chebyshev recursion extracts less spectral information from H than time evolution algorithms when fixing a given amount of created entanglement.