Skip to content
DraconiticResearch
Search Sources API
197,768 studies31 sourcesUpdated 54 min ago
Peer-reviewedCC BYSciPost Physics

Solving the 4 × 4 quantum Yang-Baxter equation

  • Marius de Leeuw1
  • Vera Posch1
  1. 1Trinity College Dublin
Open at sourceDOICite

Abstract

In this paper, we complete the classification of 4×4 4 × 4 analytic solutions of the Yang–Baxter equation. Regular solutions were recently classified and in this paper we find the remaining non-regular solutions. We present several new solutions, then consider regular and non-regular Lax operators and study their relation to the quantum Yang–Baxter equation. We show that for regular solutions there is a correspondence, which is lost in the non-regular case. In particular, we find non-regular Lax operators whose R R -matrix from the fundamental commutation relations is regular but does not satisfy the Yang-Baxter equation. These R R -matrices satisfy a modified Yang–Baxter equation instead.

Related

  1. A solution to the quantum Yang--Baxter equation associated with a universal two-valued algebraic group
    Victor M. Buchstaber
    arXivPreprintarXiv licenceFull textMathematical physicsStatistical & nonlinear physicsarXiv
  2. NS-Leibniz bialgebras, the Yang--Baxter equation and relative Rota--Baxter operators
    Bei Li, Dingguo Wang
    arXivPreprintarXiv licenceFull textAlgebra & number theoryarXiv
  3. Gaussian solutions to the Yang--Baxter equation and their twists
    Yasmeen S. Baki, Padmini Veerapen
    arXivPreprintCC BY 4.0Full textAlgebra & number theoryarXiv
  4. Dual Reflection Groups from Solutions to the Yang--Baxter Equation
    Simon Crawford
    arXivPreprintarXiv licenceFull textAlgebra & number theoryarXiv
  5. A categorical approach to the set-theoretic Yang-Baxter equation
    A. L. Agore, A. Chirvasitu, G. Militaru
    arXivPreprintarXiv licenceFull textAlgebra & number theoryarXiv

Cite

BibTeXRIS
BibTeX
@article{leeuw2026solving,
  title = {{Solving the $4 \times 4$ quantum Yang-Baxter equation}},
  author = {Marius de Leeuw and Vera Posch},
  journal = {SciPost Physics},
  year = {2026},
  month = sep,
  doi = {10.21468/scipostphys.21.3.060},
  url = {https://doi.org/10.21468/scipostphys.21.3.060},
  note = {CC BY},
}
RIS
TY  - JOUR
TI  - Solving the 4 × 4 quantum Yang-Baxter equation
AU  - Marius de Leeuw
AU  - Vera Posch
PY  - 2026
DA  - 2026/09/10
JO  - SciPost Physics
DO  - 10.21468/scipostphys.21.3.060
UR  - https://doi.org/10.21468/scipostphys.21.3.060
AB  - In this paper, we complete the classification of 4×4 4 × 4 analytic solutions of the Yang–Baxter equation. Regular solutions were recently classified and in this paper we find the remaining non-regular solutions. We present several new solutions, then consider regular and non-regular Lax operators and study their relation to the quantum Yang–Baxter equation. We show that for regular solutions there is a correspondence, which is lost in the non-regular case. In particular, we find non-regular Lax operators whose R R -matrix from the fundamental commutation relations is regular but does not satisfy the Yang-Baxter equation. These R R -matrices satisfy a modified Yang–Baxter equation instead.
SN  - 2542-4653
ER  -