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...
Saved in:
| Main Authors: | , , , , , , |
|---|---|
| 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 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1850180738314403840 |
|---|---|
| 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. |
| format | Article |
| id | doaj-art-a5e054719e8d48a096d4ec4ab1a3f71e |
| institution | OA Journals |
| issn | 2643-1564 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | American Physical Society |
| record_format | Article |
| 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 |
| work_keys_str_mv | AT selinadirnbock overcompleteintermediaterepresentationoftwoparticlegreensfunctionsanditsrelationtopartialspectralfunctions AT seungsupblee overcompleteintermediaterepresentationoftwoparticlegreensfunctionsanditsrelationtopartialspectralfunctions AT fabianbkugler overcompleteintermediaterepresentationoftwoparticlegreensfunctionsanditsrelationtopartialspectralfunctions AT sebastianhuber overcompleteintermediaterepresentationoftwoparticlegreensfunctionsanditsrelationtopartialspectralfunctions AT janvondelft overcompleteintermediaterepresentationoftwoparticlegreensfunctionsanditsrelationtopartialspectralfunctions AT karstenheld overcompleteintermediaterepresentationoftwoparticlegreensfunctionsanditsrelationtopartialspectralfunctions AT markuswallerberger overcompleteintermediaterepresentationoftwoparticlegreensfunctionsanditsrelationtopartialspectralfunctions |