Determinant form of correlators in high rank integrable spin chains via separation of variables

Nikolay Gromov; Fedor Levkovich-Maslyuk; Paul Ryan

doi:10.1007/JHEP05(2021)169

Determinant form of correlators in high rank integrable spin chains via separation of variables

Nikolay Gromov, Fedor Levkovich-Maslyuk^*, Paul Ryan

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

12 Citations (Scopus)

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Abstract

In this paper we take further steps towards developing the separation of variables program for integrable spin chains with 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.

Original language	English
Article number	169
Journal	Journal of High Energy Physics
Volume	2021
Issue number	5
Early online date	19 May 2021
DOIs	https://doi.org/10.1007/JHEP05(2021)169
Publication status	Published - May 2021

Keywords

Bethe Ansatz
Lattice Integrable Models

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10.1007/JHEP05(2021)169

Determinant form_GROMOV_Accepted 28 April 2021_GOLD_VoRAccepted author manuscript, 1.24 MBLicence: CC BY

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N2 - In this paper we take further steps towards developing the separation of variables program for integrable spin chains with 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.

AB - In this paper we take further steps towards developing the separation of variables program for integrable spin chains with 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.

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KW - Lattice Integrable Models

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DO - 10.1007/JHEP05(2021)169

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JO - Journal of High Energy Physics

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Determinant form of correlators in high rank integrable spin chains via separation of variables

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