Quantum Integrable 1D anyonic Models: Construction through Braided Yang-Baxter Equation

TL;DR

This paper constructs new quantum integrable 1D anyonic models using the braided Yang-Baxter equation, expanding the class of solvable models with potential applications in quantum many-body physics.

Contribution

It introduces novel lattice and field models of anyons, including q-anyon models and nonlinear Schrödinger equations involving anyonic operators, using the braided Yang-Baxter framework.

Findings

Discovered new lattice anyonic models

Developed q-anyon models with integrability

Derived NLS and derivative NLS quantum field models with anyonic operators

Abstract

Applying braided Yang-Baxter equation quantum integrable and Bethe ansatz solvable 1D anyonic lattice and field models are constructed. Along with known models we discover novel lattice anyonic and $q$-anyonic models as well as nonlinear Schr\"odinger equation (NLS) and the derivative NLS quantum field models involving anyonic operators, $N$-particle sectors of which yield the well known anyon gases, interacting through $\delta$ and derivative $\delta$-function potentials.