Form factors and complete spectrum of XXX antiperiodic higher spin chains by quantum separation of variables

Abstract

The antiperiodic transfer matrix associated to higher spin representations of the rational 6-vertex Yang-Baxter algebra is analyzed by generalizing the approach introduced recently in [1], for the cyclic representations, in [2], for the spin-1/2 highest weight representations, and in [3], for the spin 1/2 representations of the reflection algebra. Here, we derive the complete characterization of the transfer matrix spectrum and we prove its simplicity in the framework of Sklyanin's quantum separation of variables (SOV). Then, the characterization of local operators by Sklyanin's quantum separate variables and the expression of the scalar products of separates states by determinant formulae allow to compute the form factors of the local spin operators by one determinant formulae similar to the scalar product ones. Finally, let us comment that these results represent the SOV analogous in the antiperiodic higher spin XXX quantum chains of the results obtained for the periodic chains in [4] in the framework of the algebraic Bethe ansatz.

20 pages, introduction improved by taking into account some relevant references on the spectrum of the model under general boundary conditions, no further relevant modifications

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Cited by in corpus (33)

• Complete spectrum and scalar products for the open spin-1/2 XXZ quantum chains with non-diagonal boundary terms
• The open XXX spin chain in the SoV framework: scalar product of separate states
• On quantum separation of variables
• Open spin chains with generic integrable boundaries: Baxter equation and Bethe ansatz completeness from SOV
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• The hexagon in the mirror: the three-point function in the SoV representation
• Separation of variables and scalar products at any rank
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• Complete spectrum of quantum integrable lattice models associated to Y(gl(n)) by separation of variables
• On the form factors of local operators in the Bazhanov-Stroganov and chiral Potts models
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• Iterative construction of eigenfunctions of the monodromy matrix for SL(2,C) magnet
• The open XXZ spin chain in the SoV framework: scalar product of separate states
• A new integral representation for the scalar products of Bethe states for the XXX spin chain
• Exact solution of the spin-s Heisenberg chain with generic non-diagonal boundaries
• Transfer matrix spectrum for cyclic representations of the 6-vertex reflection algebra II
• On Scalar Products in Higher Rank Quantum Separation of Variables
• Reflection algebra and functional equations
• On quantum separation of variables beyond fundamental representations
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• On Separation of Variables for Reflection Algebras
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• Correlation functions by Separation of Variables: the XXX spin chain
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• Separation of variables for higher rank integrable models: review of recent progress
• Bethe States of the integrable spin-s chain with generic open boundaries
• The open XYZ spin 1/2 chain: Separation of Variables and scalar products for boundary fields related by a constraint