Determinant Form of Correlators in High Rank Integrable Spin Chains via\n Separation of Variables

Abstract

In this paper we take further steps towards developing the separation of\nvariables program for integrable spin chains with gl(N) symmetry. By finding,\nfor the first time, the matrix elements of the SoV measure explicitly we were\nable to compute correlation functions and wave function overlaps in a simple\ndeterminant form. In particular, we show how an overlap between on-shell and\noff-shell algebraic Bethe states can be written as a determinant. Another\nresult, particularly useful for AdS/CFT applications, is an overlap between two\nBethe states with different twists, which also takes a determinant form in our\napproach. Our results also extend our previous works in collaboration with A.\nCavaglia and D. Volin to general values of the spin, including the SoV\nconstruction in the higher-rank non-compact case for the first time.\n