English

Vertex operator approach to semi-infinite spin chain : recent progress

Exactly Solvable and Integrable Systems 2019-02-13 v1 Statistical Mechanics High Energy Physics - Theory Mathematical Physics math.MP Quantum Algebra

Abstract

Vertex operator approach is a powerful method to study exactly solvable models. We review recent progress of vertex operator approach to semi-infinite spin chain. (1) The first progress is a generalization of boundary condition. We study Uq(sl^(2))U_q(\widehat{sl}(2)) spin chain with a triangular boundary, which gives a generalization of diagonal boundary [Baseilhac and Belliard 2013, Baseilhac and Kojima 2014]. We give a bosonization of the boundary vacuum state. As an application, we derive a summation formulae of boundary magnetization. (2) The second progress is a generalization of hidden symmetry. We study supersymmetry Uq(sl^(MN))U_q(\widehat{sl}(M|N)) spin chain with a diagonal boundary [Kojima 2013]. By now we have studied spin chain with a boundary, associated with symmetry Uq(sl^(N))U_q(\widehat{sl}(N)), Uq(A2(2))U_q(A_2^{(2)}) and Uq,p(sl^(N))U_{q,p}(\widehat{sl}(N)) [Furutsu-Kojima 2000, Yang-Zhang 2001, Kojima 2011, Miwa-Weston 1997, Kojima 2011], where bosonizations of vertex operators are realized by "monomial" . However the vertex operator for Uq(sl^(MN))U_q(\widehat{sl}(M|N)) is realized by "sum", a bosonization of boundary vacuum state is realized by "monomial".

Keywords

Cite

@article{arxiv.1404.5747,
  title  = {Vertex operator approach to semi-infinite spin chain : recent progress},
  author = {Takeo Kojima},
  journal= {arXiv preprint arXiv:1404.5747},
  year   = {2019}
}

Comments

Proceedings of 10-th Lie Theory and its Applications in Physics, LaTEX, 10 pages

R2 v1 2026-06-22T03:56:44.519Z