Abstract
We study the matrix product state which appears as the boundary state of the AdS/dCFT set-up where a probe D7 brane wraps two two-spheres stabilized by fluxes. The matrix product state plays a dual role, on one hand acting as a tool for computing one-point functions in a domain wall version of N=4 SYM and on the other hand acting as the initial state in the study of quantum quenches of the Heisenberg spin chain. We derive a number of selection rules for the overlaps between the matrix product state and the eigenstates of the Heisenberg spin chain and in particular demonstrate that the matrix product state does not fulfil a recently proposed integrability criterion. Accordingly, we find that the overlaps can not be expressed in the usual factorized determinant form. Nevertheless, we derive some exact results for one-point functions of simple operators and present a closed formula for one-point functions of more general operators in the limit of large spin-chain length.
Highlights
Exact results for overlaps between states in integrable spin chains have important applications in the calculation of correlation functions in supersymmetric gauge theories as well as in the study of quantum quenches in statistical physics
From the point of view of the AdS/dCFT correspondence, overlaps between Bethe eigenstates and specific matrix product states encode information about one-point functions in domain wall versions of N = 4 SYM theory [1,2,3,4,5] and in statistical physics the same matrix product states play the role of the initial state of a quantum quench [6,7,8]
With the present investigations we have completed the analysis of the integrability structure of matrix product states of relevance for one-point functions in defect versions of N = 4 SYM based on probe-brane set-ups with fluxes
Summary
Exact results for overlaps between states in integrable spin chains have important applications in the calculation of correlation functions in supersymmetric gauge theories as well as in the study of quantum quenches in statistical physics. For Bethe states with paired roots the determinant of the Gaudin matrix factorizes as det G = det G+ det G−,. These observations lead the authors of [11] to suggest that matrix product states should be denoted as integrable when annihilated by all odd charges of the spin chain and in that case would play a role analogous to that of the integrable boundary states of Zamolodnikov for continuum quantum field theories [12]. In [13] integrable matrix product states were related
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