Determinant form of correlators in high rank integrable spin chains via separation of variables
Abstract In this paper we take further steps towards developing the separation of variables program for integrable spin chains with gl N $$ \mathfrak{gl}(N) $$ symmetry. By finding, for the first time, the matrix elements of the SoV measure explicitly we were able to compute correlation functions an...
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Online Access: | https://doi.org/10.1007/JHEP05(2021)169 |
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doaj-f22b343900994af9bb325d7e8113caac2021-05-23T11:07:14ZengSpringerOpenJournal of High Energy Physics1029-84792021-05-012021518110.1007/JHEP05(2021)169Determinant form of correlators in high rank integrable spin chains via separation of variablesNikolay Gromov0Fedor Levkovich-Maslyuk1Paul Ryan2Mathematics Department, King’s College LondonInstitut de Physique Théorique, Université Paris Saclay, CEA, CNRSSchool of Mathematics & Hamilton Mathematics Institute, Trinity College DublinAbstract In this paper we take further steps towards developing the separation of variables program for integrable spin chains with gl N $$ \mathfrak{gl}(N) $$ symmetry. By finding, for the first time, the matrix elements of the SoV measure explicitly we were able to compute correlation functions and wave function overlaps in a simple determinant form. In particular, we show how an overlap between on-shell and off-shell algebraic Bethe states can be written as a determinant. Another result, particularly useful for AdS/CFT applications, is an overlap between two Bethe states with different twists, which also takes a determinant form in our approach. Our results also extend our previous works in collaboration with A. Cavaglia and D. Volin to general values of the spin, including the SoV construction in the higher-rank non-compact case for the first time.https://doi.org/10.1007/JHEP05(2021)169Bethe AnsatzLattice Integrable Models |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Nikolay Gromov Fedor Levkovich-Maslyuk Paul Ryan |
spellingShingle |
Nikolay Gromov Fedor Levkovich-Maslyuk Paul Ryan Determinant form of correlators in high rank integrable spin chains via separation of variables Journal of High Energy Physics Bethe Ansatz Lattice Integrable Models |
author_facet |
Nikolay Gromov Fedor Levkovich-Maslyuk Paul Ryan |
author_sort |
Nikolay Gromov |
title |
Determinant form of correlators in high rank integrable spin chains via separation of variables |
title_short |
Determinant form of correlators in high rank integrable spin chains via separation of variables |
title_full |
Determinant form of correlators in high rank integrable spin chains via separation of variables |
title_fullStr |
Determinant form of correlators in high rank integrable spin chains via separation of variables |
title_full_unstemmed |
Determinant form of correlators in high rank integrable spin chains via separation of variables |
title_sort |
determinant form of correlators in high rank integrable spin chains via separation of variables |
publisher |
SpringerOpen |
series |
Journal of High Energy Physics |
issn |
1029-8479 |
publishDate |
2021-05-01 |
description |
Abstract In this paper we take further steps towards developing the separation of variables program for integrable spin chains with gl N $$ \mathfrak{gl}(N) $$ symmetry. By finding, for the first time, the matrix elements of the SoV measure explicitly we were able to compute correlation functions and wave function overlaps in a simple determinant form. In particular, we show how an overlap between on-shell and off-shell algebraic Bethe states can be written as a determinant. Another result, particularly useful for AdS/CFT applications, is an overlap between two Bethe states with different twists, which also takes a determinant form in our approach. Our results also extend our previous works in collaboration with A. Cavaglia and D. Volin to general values of the spin, including the SoV construction in the higher-rank non-compact case for the first time. |
topic |
Bethe Ansatz Lattice Integrable Models |
url |
https://doi.org/10.1007/JHEP05(2021)169 |
work_keys_str_mv |
AT nikolaygromov determinantformofcorrelatorsinhighrankintegrablespinchainsviaseparationofvariables AT fedorlevkovichmaslyuk determinantformofcorrelatorsinhighrankintegrablespinchainsviaseparationofvariables AT paulryan determinantformofcorrelatorsinhighrankintegrablespinchainsviaseparationofvariables |
_version_ |
1721430243490660352 |