Correlation functions of the XXZ spin chain with the twisted boundary condition

Qiao, Yi; Xin, Zhirong; Xu, Xiaotian; Hao, Kun; Yang, Tao; Cao, Junpeng; Yang, Wen-Li

doi:10.1063/1.5113651

Cited by 1 publication

(1 citation statement)

References 37 publications

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“…It happens that, for a large class of quantum integrable models solved by SoV, the scalar products of the separate states can be generically expressed as determinants of a dressed sum of generalized Vandermonde matrices. As a consequence, when the solution of the quantum inverse problem is known, form factors can also often be expressed in terms of similar determinants (see for instance [68,71,73,74,78,97]). Such determinants depend however in a non-trivial way on the inhomogeneity parameters (the latter label the rows or columns), and cannot be easily used for the study of the physical model.…”

Section: Introductionmentioning

confidence: 99%

On scalar products and form factors by separation of variables: the antiperiodic XXZ model

Pei¹,

Terras²

2021

J. Phys. A: Math. Theor.

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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.

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