On the quantum inverse scattering problem

TL;DR

This paper presents a general method for reconstructing local quantum operators from the quantum monodromy matrix in integrable lattice models, applicable to various models including those with impurities and higher spins.

Contribution

The paper introduces a universal approach to solve the quantum inverse scattering problem for a broad class of lattice models, extending previous methods to more complex and generalized systems.

Findings

Applicable to models with impurities and fused lattice models

Successfully applied to sl(n) XXZ, XYZ, and spin-s Heisenberg chains

Provides a unified framework for reconstructing local operators

Abstract

A general method for solving the so-called quantum inverse scattering problem (namely the reconstruction of local quantum (field) operators in term of the quantum monodromy matrix satisfying a Yang-Baxter quadratic algebra governed by an R-matrix) for a large class of lattice quantum integrable models is given. The principal requirement being the initial condition (R(0) = P, the permutation operator) for the quantum R-matrix solving the Yang-Baxter equation, it applies not only to most known integrable fundamental lattice models (such as Heisenberg spin chains) but also to lattice models with arbitrary number of impurities and to the so-called fused lattice models (including integrable higher spin generalizations of Heisenberg chains). Our method is then applied to several important examples like the sl(n) XXZ model, the XYZ spin-1/2 chain and also to the spin-s Heisenberg chains.