Exact Bethe ansatz solution of nonultralocal quantum mKdV model

TL;DR

This paper introduces an exact quantum solution for the nonultralocal mKdV model using algebraic Bethe ansatz, establishing its integrability and connection to the XXZ spin chain, advancing understanding of nonultralocal quantum integrable systems.

Contribution

It provides the first exact Bethe ansatz solution for the nonultralocal quantum mKdV model, including the construction of its Lax operator, R and Z matrices, and proof of integrability.

Findings

Exact eigenvalues obtained via algebraic Bethe ansatz.

Connection established between quantum mKdV and spin-1/2 XXZ chain.

Model's integrability confirmed through braided quantum Yang-Baxter equation.

Abstract

A lattice regularized Lax operator for the nonultralocal modified Korteweg de Vries (mKdV) equation is proposed at the quantum level with the basic operators satisfying a $q$-deformed braided algebra. Finding further the associated quantum $R$ and $Z$-matrices the exact integrability of the model is proved through the braided quantum Yang--Baxter equation, a suitably generalized equation for the nonultralocal models. Using the algebraic Bethe ansatz the eigenvalue problem of the quantum mKdV model is exactly solved and its connection with the spin-$\ha$ XXZ chain is established, facilitating the investigation of the corresponding conformal properties.