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

TL;DR

This paper advances the separation of variables method for high-rank integrable spin chains, explicitly computing matrix elements and expressing correlation functions and overlaps as determinants, with applications to AdS/CFT.

Contribution

First explicit computation of the SoV measure matrix elements enabling determinant formulas for correlation functions and Bethe state overlaps in high-rank integrable spin chains.

Findings

Determinant formulas for correlation functions and overlaps.

Explicit SoV measure matrix elements.

Extension to higher-rank non-compact cases.

Abstract

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