Spectral functions and time evolution from the Chebyshev recursion

Wolf, F. Alexander, Justiniano, Jorge A, Mcculloch, Ian P and Schollwock, Ulrich (2015) Spectral functions and time evolution from the Chebyshev recursion. Physical Review B - Condensed Matter and Materials Physics, 91 115144: 115144-1-115144-17. doi:10.1103/PhysRevB.91.115144

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Author Wolf, F. Alexander
Justiniano, Jorge A
Mcculloch, Ian P
Schollwock, Ulrich
Title Spectral functions and time evolution from the Chebyshev recursion
Journal name Physical Review B - Condensed Matter and Materials Physics   Check publisher's open access policy
ISSN 1550-235X
1098-0121
Publication date 2015-03-31
Year available 2015
Sub-type Article (original research)
DOI 10.1103/PhysRevB.91.115144
Open Access Status File (Publisher version)
Volume 91
Issue 115144
Start page 115144-1
End page 115144-17
Total pages 17
Place of publication College Park, United States
Publisher American Physical Society
Language eng
Subject 2504 Electronic, Optical and Magnetic Materials
3104 Condensed Matter Physics
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 similar to 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 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.
Formatted 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 ~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 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.
Keyword Physics, Condensed Matter
Physics
Q-Index Code C1
Q-Index Status Confirmed Code
Grant ID FOR 1807
CE110001013
Institutional Status UQ

Document type: Journal Article
Sub-type: Article (original research)
Collections: School of Mathematics and Physics
Official 2016 Collection
 
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