Overcomplete intermediate representation of two-particle Green's functions and its relation to partial spectral functions

Two-particle response functions are a centerpiece of both experimental and theoretical quantum many-body physics. Yet, due to their size and discontinuity structure, they are challenging to handle numerically. Recently, two advances were made to tackle this problem: first, the overcomplete intermedi...

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Main Authors: Selina Dirnböck, Seung-Sup B. Lee, Fabian B. Kugler, Sebastian Huber, Jan von Delft, Karsten Held, Markus Wallerberger
Format: Article
Language:English
Published: American Physical Society 2024-12-01
Series:Physical Review Research
Online Access:http://doi.org/10.1103/PhysRevResearch.6.043228
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author Selina Dirnböck
Seung-Sup B. Lee
Fabian B. Kugler
Sebastian Huber
Jan von Delft
Karsten Held
Markus Wallerberger
author_facet Selina Dirnböck
Seung-Sup B. Lee
Fabian B. Kugler
Sebastian Huber
Jan von Delft
Karsten Held
Markus Wallerberger
author_sort Selina Dirnböck
collection DOAJ
description Two-particle response functions are a centerpiece of both experimental and theoretical quantum many-body physics. Yet, due to their size and discontinuity structure, they are challenging to handle numerically. Recently, two advances were made to tackle this problem: first, the overcomplete intermediate representation (OIR), which provides a highly efficient compression of Green's functions in imaginary frequency, and second, partial spectral functions (PSFs), which allow for an efficient evaluation in real frequency. We show that there is a two-to-one correspondence between PSFs and OIR coefficients and exploit this fact to construct the OIR for three-or-more-particle propagators. We then use OIR to fit and compress imaginary-frequency data obtained from the numerical renormalization group (NRG), reaching a compression ratio of more than 400. Finally, we attempt to match the OIR data to partial Green's functions from NRG. Due to the overcompleteness, we achieve only qualitative agreement.
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publishDate 2024-12-01
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series Physical Review Research
spelling doaj-art-a5e054719e8d48a096d4ec4ab1a3f71e2025-08-20T02:18:03ZengAmerican Physical SocietyPhysical Review Research2643-15642024-12-016404322810.1103/PhysRevResearch.6.043228Overcomplete intermediate representation of two-particle Green's functions and its relation to partial spectral functionsSelina DirnböckSeung-Sup B. LeeFabian B. KuglerSebastian HuberJan von DelftKarsten HeldMarkus WallerbergerTwo-particle response functions are a centerpiece of both experimental and theoretical quantum many-body physics. Yet, due to their size and discontinuity structure, they are challenging to handle numerically. Recently, two advances were made to tackle this problem: first, the overcomplete intermediate representation (OIR), which provides a highly efficient compression of Green's functions in imaginary frequency, and second, partial spectral functions (PSFs), which allow for an efficient evaluation in real frequency. We show that there is a two-to-one correspondence between PSFs and OIR coefficients and exploit this fact to construct the OIR for three-or-more-particle propagators. We then use OIR to fit and compress imaginary-frequency data obtained from the numerical renormalization group (NRG), reaching a compression ratio of more than 400. Finally, we attempt to match the OIR data to partial Green's functions from NRG. Due to the overcompleteness, we achieve only qualitative agreement.http://doi.org/10.1103/PhysRevResearch.6.043228
spellingShingle Selina Dirnböck
Seung-Sup B. Lee
Fabian B. Kugler
Sebastian Huber
Jan von Delft
Karsten Held
Markus Wallerberger
Overcomplete intermediate representation of two-particle Green's functions and its relation to partial spectral functions
Physical Review Research
title Overcomplete intermediate representation of two-particle Green's functions and its relation to partial spectral functions
title_full Overcomplete intermediate representation of two-particle Green's functions and its relation to partial spectral functions
title_fullStr Overcomplete intermediate representation of two-particle Green's functions and its relation to partial spectral functions
title_full_unstemmed Overcomplete intermediate representation of two-particle Green's functions and its relation to partial spectral functions
title_short Overcomplete intermediate representation of two-particle Green's functions and its relation to partial spectral functions
title_sort overcomplete intermediate representation of two particle green s functions and its relation to partial spectral functions
url http://doi.org/10.1103/PhysRevResearch.6.043228
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