Solutions of quantum Yang-Baxter equation related to $U_q (gl(2))$ algebra and associated integrable lattice models

TL;DR

This paper constructs new solutions to the quantum Yang-Baxter equation using a coloured braid group representation linked to the quantum algebra $U_q(gl(2))$, leading to integrable lattice models with novel properties.

Contribution

It introduces a coloured braid group representation based on a modified universal R-matrix and derives new solutions to the quantum Yang-Baxter equation through Yang-Baxterisation, connecting to integrable lattice models.

Findings

New solutions of quantum Yang-Baxter equation related to $U_q(gl(2))$

Explicit realization of FRT algebra for the CBGR

Lax operators for extended integrable lattice models

Abstract

A coloured braid group representation (CBGR) is constructed with the help of some modified universal ${\cal R}$-matrix, associated to $U_q(gl(2))$ quantised algebra. Explicit realisation of Faddeev-Reshetikhin-Takhtajan (FRT) algebra is built up for this CBGR and new solutions of quantum Yang-Baxter equation are subsequently found through Yang-Baxterisation of FRT algebra. These solutions are interestingly related to nonadditive type quantum $R$-matrix and have a nontrivial $q\rightarrow 1$ limit. Lax operators of several concrete integrable models, which may be considered as some `coloured' extensions of lattice nonlinear Schr${\ddot {\rm o}}$dinger model and Toda chain, are finally obtained by taking different reductions of such solutions.