How to Draw a Correlation Function
We discuss the connection between the 0 Heisenberg spin chain and some aspects of enumerative combinatorics. The representation of the Bethe wave functions via the Schur functions allows us to apply the theory of symmetric functions to the calculation of the correlation functions. We provide a combi...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2021 |
| Main Authors: | , |
| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2021
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/211421 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | How to Draw a Correlation Function. Nikolay Bogoliubov and Cyril Malyshev. SIGMA 17 (2021), 106, 35 pages |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862741837877346304 |
|---|---|
| author | Bogoliubov, Nikolay Malyshev, Cyril |
| author_facet | Bogoliubov, Nikolay Malyshev, Cyril |
| citation_txt | How to Draw a Correlation Function. Nikolay Bogoliubov and Cyril Malyshev. SIGMA 17 (2021), 106, 35 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | We discuss the connection between the 0 Heisenberg spin chain and some aspects of enumerative combinatorics. The representation of the Bethe wave functions via the Schur functions allows us to apply the theory of symmetric functions to the calculation of the correlation functions. We provide a combinatorial derivation of the dynamical auto-correlation functions and visualise them in terms of nests of self-avoiding lattice paths. Asymptotics of the auto-correlation functions are obtained in the double scaling limit, provided that the evolution parameter is large.
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| first_indexed | 2026-04-17T18:04:08Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-211421 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-04-17T18:04:08Z |
| publishDate | 2021 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Bogoliubov, Nikolay Malyshev, Cyril 2026-01-02T08:29:26Z 2021 How to Draw a Correlation Function. Nikolay Bogoliubov and Cyril Malyshev. SIGMA 17 (2021), 106, 35 pages 1815-0659 2020 Mathematics Subject Classification: 05A19; 05E05; 82B23 arXiv:2112.04733 https://nasplib.isofts.kiev.ua/handle/123456789/211421 https://doi.org/10.3842/SIGMA.2021.106 We discuss the connection between the 0 Heisenberg spin chain and some aspects of enumerative combinatorics. The representation of the Bethe wave functions via the Schur functions allows us to apply the theory of symmetric functions to the calculation of the correlation functions. We provide a combinatorial derivation of the dynamical auto-correlation functions and visualise them in terms of nests of self-avoiding lattice paths. Asymptotics of the auto-correlation functions are obtained in the double scaling limit, provided that the evolution parameter is large. This work was supported by the Russian Science Foundation (Grant 18-11-00297). We are grateful to the referees for their comments and suggestions, which enabled us to improve the paper. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications How to Draw a Correlation Function Article published earlier |
| spellingShingle | How to Draw a Correlation Function Bogoliubov, Nikolay Malyshev, Cyril |
| title | How to Draw a Correlation Function |
| title_full | How to Draw a Correlation Function |
| title_fullStr | How to Draw a Correlation Function |
| title_full_unstemmed | How to Draw a Correlation Function |
| title_short | How to Draw a Correlation Function |
| title_sort | how to draw a correlation function |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/211421 |
| work_keys_str_mv | AT bogoliubovnikolay howtodrawacorrelationfunction AT malyshevcyril howtodrawacorrelationfunction |