Determinant Form of Correlators in High Rank Integrable Spin Chains via Separation of Variables

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 s...

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Bibliographic Details
Published in:arXiv.org 2020-11
Main Authors: Gromov, Nikolay, Levkovich-Maslyuk, Fedor, Ryan, Paul
Format: Article
Language:English
Subjects:
Chains
Correlators
Matrix methods
Separation
Wave functions
Online Access:Get full text
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Summary: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.
ISSN:2331-8422
DOI:10.48550/arxiv.2011.08229