Form-factors and complete basis of observables via separation of variables for higher rank spin chains
Abstract Integrable sl $$ \mathfrak{sl} $$ (N) spin chains, which we consider in this paper, are not only the prototypical example of quantum integrable systems but also systems with a wide range of applications. For these models we use the Functional Separation of Variables (FSoV) technique with a...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2022-11-01
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| Series: | Journal of High Energy Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1007/JHEP11(2022)039 |
| _version_ | 1797865668042817536 |
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| author | Nikolay Gromov Nicolò Primi Paul Ryan |
| author_facet | Nikolay Gromov Nicolò Primi Paul Ryan |
| author_sort | Nikolay Gromov |
| collection | DOAJ |
| description | Abstract Integrable sl $$ \mathfrak{sl} $$ (N) spin chains, which we consider in this paper, are not only the prototypical example of quantum integrable systems but also systems with a wide range of applications. For these models we use the Functional Separation of Variables (FSoV) technique with a new tool called Character Projection to compute all matrix elements of a complete set of operators, which we call principal operators, in the basis diagonalising the tower of conserved charges as determinants in Q-functions. Building up on these results we then derive similar determinant forms for the form-factors of combinations of multiple principal operators between arbitrary factorizable states, which include, in particular, off-shell Bethe vectors and Bethe vectors with arbitrary twists. We prove that the set of principal operators generates the complete spin chain Yangian. Furthermore, we derive the representation of these operators in the SoV bases allowing one to compute correlation functions with an arbitrary number of principal operators. Finally, we show that the available combinations of multiple insertions includes Sklyanin’s SoV B operator. As a result, we are able to derive the B operator for sl $$ \mathfrak{sl} $$ (N) spin chains using a minimal set of ingredients, namely the FSoV method and the structure of the SoV basis. |
| first_indexed | 2024-04-09T23:12:58Z |
| format | Article |
| id | doaj.art-4f5e270acda344b89a0bca1d27258e7d |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-04-09T23:12:58Z |
| publishDate | 2022-11-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-4f5e270acda344b89a0bca1d27258e7d2023-03-22T10:16:50ZengSpringerOpenJournal of High Energy Physics1029-84792022-11-0120221115510.1007/JHEP11(2022)039Form-factors and complete basis of observables via separation of variables for higher rank spin chainsNikolay Gromov0Nicolò Primi1Paul Ryan2Mathematics Department, King’s College LondonMathematics Department, King’s College LondonMathematics Department, King’s College LondonAbstract Integrable sl $$ \mathfrak{sl} $$ (N) spin chains, which we consider in this paper, are not only the prototypical example of quantum integrable systems but also systems with a wide range of applications. For these models we use the Functional Separation of Variables (FSoV) technique with a new tool called Character Projection to compute all matrix elements of a complete set of operators, which we call principal operators, in the basis diagonalising the tower of conserved charges as determinants in Q-functions. Building up on these results we then derive similar determinant forms for the form-factors of combinations of multiple principal operators between arbitrary factorizable states, which include, in particular, off-shell Bethe vectors and Bethe vectors with arbitrary twists. We prove that the set of principal operators generates the complete spin chain Yangian. Furthermore, we derive the representation of these operators in the SoV bases allowing one to compute correlation functions with an arbitrary number of principal operators. Finally, we show that the available combinations of multiple insertions includes Sklyanin’s SoV B operator. As a result, we are able to derive the B operator for sl $$ \mathfrak{sl} $$ (N) spin chains using a minimal set of ingredients, namely the FSoV method and the structure of the SoV basis.https://doi.org/10.1007/JHEP11(2022)039Bethe AnsatzLattice Integrable Models |
| spellingShingle | Nikolay Gromov Nicolò Primi Paul Ryan Form-factors and complete basis of observables via separation of variables for higher rank spin chains Journal of High Energy Physics Bethe Ansatz Lattice Integrable Models |
| title | Form-factors and complete basis of observables via separation of variables for higher rank spin chains |
| title_full | Form-factors and complete basis of observables via separation of variables for higher rank spin chains |
| title_fullStr | Form-factors and complete basis of observables via separation of variables for higher rank spin chains |
| title_full_unstemmed | Form-factors and complete basis of observables via separation of variables for higher rank spin chains |
| title_short | Form-factors and complete basis of observables via separation of variables for higher rank spin chains |
| title_sort | form factors and complete basis of observables via separation of variables for higher rank spin chains |
| topic | Bethe Ansatz Lattice Integrable Models |
| url | https://doi.org/10.1007/JHEP11(2022)039 |
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