Year: 2015
Type: article
Abstract: 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 $\ensuremath{\sim}\frac{1}{6}$. 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 ${e}^{\ensuremath{-}iHt}$ 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 the 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.
Source: Physical Review B
Language: English
Topic: Quantum many-body systems
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
Awards: G1252056419, G2393098246
OpenAlex ID: W1998730500