On scalar products and form factors by Separation of Variables: the antiperiodic XXZ model

Abstract

We consider the XXZ spin-1/2 Heisenberg chain with antiperiodic boundary conditions. The inhomogeneous version of this model can be solved by Separation of Variables (SoV), and the eigenstates can be constructed in terms of Q-functions, solution of a Baxter TQ-equation, which have double periodicity compared to the periodic case. We compute in this framework the scalar products of a particular class of separate states which notably includes the eigenstates of the transfer matrix. We also compute the form factors of local spin operators, i.e. their matrix elements between two eigenstates of the transfer matrix. We show that these quantities admit determinant representations with rows and columns labelled by the roots of the Q-functions of the corresponding separate states, as in the periodic case, although the form of the determinant are here slightly different. We also propose alternative types of determinant representations written directly in terms of the transfer matrix eigenvalues.

40 pages, important corrections in the computations and in the final formulas, new alternative representations added

References in corpus (10)

• Hidden Grassmann Structure in the XXZ Model II: Creation Operators
• Antiperiodic spin-1/2 XXZ quantum chains by separation of variables: Complete spectrum and form factors
• Correlation functions of the open XXZ chain I
• Separation of Variables in the open XXX chain
• Modified algebraic Bethe ansatz for XXZ chain on the segment - I - triangular cases
• Modified algebraic Bethe ansatz for XXZ chain on the segment - II - general cases
• Algebraic representation of correlation functions in integrable spin chains
• Completeness of Bethe Ansatz by Sklyanin SOV for Cyclic Representations of Integrable Quantum Models
• Transfer matrix spectrum for cyclic representations of the 6-vertex reflection algebra I
• Large-distance and long-time asymptotic behavior of the reduced density matrix in the non-linear Schrödinger model

Cited by in corpus (2)

• Separation of Variables in AdS/CFT: Functional Approach for the Fishnet CFT
• Determinant Form of Correlators in High Rank Integrable Spin Chains via Separation of Variables