Form-factors and complete basis of observables via separation of variables for higher rank spin chains

A bstract Integrable 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 C...

Full description

Saved in:
Bibliographic Details
Published in:The journal of high energy physics 2022-11, Vol.2022 (11), p.39-55, Article 39
Main Authors: Gromov, Nikolay, Primi, Nicolò, Ryan, Paul
Format: Article
Language:English
Subjects:
Bethe Ansatz
Chains
Classical and Quantum Gravitation
Construction
Determinants
Elementary Particles
High energy physics
Lattice Integrable Models
Operators (mathematics)
Physics
Physics and Astronomy
Quantum Field Theories
Quantum Field Theory
Quantum Physics
Regular Article - Theoretical Physics
Relativity Theory
Separation
String Theory
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:A bstract Integrable 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 ( N ) spin chains using a minimal set of ingredients, namely the FSoV method and the structure of the SoV basis.
ISSN:1029-8479
1029-8479
DOI:10.1007/JHEP11(2022)039