Generation of Integrable Quantum Nonultralocal Model through Braided Yang-Baxter Equation

TL;DR

This paper introduces a braided Yang-Baxter equation framework to formulate quantum integrability for nonultralocal models, unifying known models and discovering new integrable quantum nonultralocal models.

Contribution

It proposes a universal braided Yang-Baxter equation that underpins the algebraic structure of nonultralocal models, enabling derivation of existing models and discovery of new integrable models.

Findings

Unified algebraic framework for nonultralocal models

Derived new integrable quantum models like mKdV and anyonic models

Connected nonultralocal models with SUSY and reflection equations

Abstract

Formulating quantum integrability for nonultralocal models (NM) parallel to the familiar approach of inverse scattering method is a long standing problem. After reviewing our result regarding algebraic structures of ultralocal models, we look for the algebra underlying NM. We propose an universal equation represented by braided Yang-Baxter equation and able to derive all basic equations of the known models like WZWN model, nonabelian Toda chain, quantum mapping etc. As further useful application we discover new integrable quantum NM, e.g. mKdV model, anyonic model, Kundu-Eckhaus equation and derive SUSY models and reflection equation from the nonultralocal view point.