Quantum Projectors and Local Operators in Lattice Integrable Models

TL;DR

This paper develops a method to construct local operators in lattice quantum integrable models, enabling calculation of their form factors using algebraic Bethe ansatz, advancing understanding of quantum projectors and local operators.

Contribution

It introduces a new class of local operators constructed from monodromy matrix elements, related to quantum projectors, with calculable form factors in lattice models.

Findings

Constructed local operators from monodromy matrix elements.

Established commutation relations with monodromy matrix elements.

Demonstrated calculation of form factors using algebraic Bethe ansatz.

Abstract

In the framework of the quantum inverse scattering method, we consider a problem of constructing local operators for two-dimensional quantum integrable models, especially for the lattice versions of the nonlinear Schrodinger and sine-Gordon models. We show that a certain class of local operators can be constructed from the matrix elements of the monodromy matrix in a simple way. They are closely related to the quantum projectors and have nice commutation relations with the half of the matrix elements of the elementary monodromy matrix. The form factors of these operators can be calculated by using the standard algebraic Bethe ansatz techniques.