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

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.

💡 Research Summary

The paper introduces a systematic framework for constructing quantum‑integrable one‑dimensional anyonic models by employing the braided Yang‑Baxter equation (BYBE). Traditional Yang‑Baxter integrability relies on an R‑matrix that encodes bosonic or fermionic exchange statistics; it cannot directly accommodate particles whose exchange produces a non‑trivial phase factor e^{iθ}. The authors resolve this limitation by inserting a braid operator B that implements the anyonic phase into the algebraic relation, yielding the BYBE: \