Solution of the quantum inverse problem

TL;DR

This paper presents a quantum inverse problem solution by deriving a formula that expresses local operators in terms of monodromy matrix elements, applicable to various integrable models including spin chains and strongly correlated electron systems.

Contribution

It introduces a quantum analogue of the classical inverse scattering transform for fundamental graded models, enabling explicit expressions for local operators in integrable systems.

Findings

Derived a formula relating local operators to monodromy matrix elements

Applicable to models like XYZ spin chain and supersymmetric t-J model

Facilitates analysis of strongly correlated electron systems

Abstract

We derive a formula that expresses the local spin and field operators of fundamental graded models in terms of the elements of the monodromy matrix. This formula is a quantum analogue of the classical inverse scattering transform. It applies to fundamental spin chains, such as the XYZ chain, and to a number of important exactly solvable models of strongly correlated electrons, such as the supersymmetric t-J model or the the EKS model.