On exact overlaps of integrable matrix product states: inhomogeneities, twists and dressing formulas

TL;DR

This paper develops summation formulas for overlaps between integrable matrix product states and Bethe eigenstates, incorporating inhomogeneities and twists, with applications to the $SO(6)$ spin chain and ${ m N}=4$ SYM.

Contribution

It introduces a general quantum dressing approach and representation theory of twisted Yangians to derive new overlap formulas for integrable models.

Findings

Derived summation formulas involving eigenvalues of fused transfer matrices.

Applied formulas to the $SO(6)$ spin chain relevant for ${ m N}=4$ SYM.

Filled the last gap in the analytical understanding of the overlap formula.

Abstract

Invoking a quantum dressing procedure as well as the representation theory of twisted Yangians we derive a number of summation formulas for the overlap between integrable matrix product states and Bethe eigenstates which involve only eigenvalues of fused transfer matrices and which are valid in the presence of inhomogeneities as well as twists. Although the method is general we specialize to the $SO(6)$ spin chain for which integrable matrix product states corresponding to evaluation representations of the twisted Yangian $Y^+(4)$ encode the information about one-point functions of the D3-D5 domain wall version of ${\cal N}=4$ SYM. Considering the untwisted and homogeneous limit of our summation formulas we finally fill the last gap in the analytical understanding of the overlap formula for the $SO(6$) sector of the D3-D5 domain wall system.