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arXiv · 1501.07216

Spectral functions and time evolution from the Chebyshev recursion

F. Alexander Wolf·Jorge A. Justiniano·Ian P. McCulloch·Ulrich Schollwöck
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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 $\sim\frac{1}{6}$. 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 $e^{-iHt}$ 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.

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F. Alexander Wolf, Jorge A. Justiniano, Ian P. McCulloch, Ulrich Schollwöck. 2015-04-27. Spectral functions and time evolution from the Chebyshev recursion. https://doi.org/10.1103/physrevb.91.115144

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