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On scalar products and form factors by Separation of Variables: the antiperiodic XXZ model
- Source :
- J.Phys.A, J.Phys.A, 2022, 55 (1), pp.015205. ⟨10.1088/1751-8121/ac3b85⟩
- Publication Year :
- 2020
-
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.<br />40 pages, important corrections in the computations and in the final formulas, new alternative representations added
- Subjects :
- Statistics and Probability
separation of variables
Scalar (mathematics)
[PHYS.MPHY]Physics [physics]/Mathematical Physics [math-ph]
Separation of variables
FOS: Physical sciences
General Physics and Astronomy
01 natural sciences
010305 fluids & plasmas
Bethe ansatz
Matrix (mathematics)
0103 physical sciences
Boundary value problem
010306 general physics
scalar products
form factors
Eigenvalues and eigenvectors
Mathematical Physics
Mathematics
Mathematical physics
Spin-½
Nonlinear Sciences - Exactly Solvable and Integrable Systems
Statistical and Nonlinear Physics
Mathematical Physics (math-ph)
16. Peace & justice
Transfer matrix
quantum integrable systems
Modeling and Simulation
Exactly Solvable and Integrable Systems (nlin.SI)
Subjects
Details
- Language :
- English
- Database :
- OpenAIRE
- Journal :
- J.Phys.A, J.Phys.A, 2022, 55 (1), pp.015205. ⟨10.1088/1751-8121/ac3b85⟩
- Accession number :
- edsair.doi.dedup.....39361550d47bda53afc035147a5a63bc