Vertex operator approach to semi-infinite spin chain : recent progress
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 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 spin chain with a diagonal boundary [Kojima 2013]. By now we have studied spin chain with a boundary, associated with symmetry , and [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 is realized by "sum", a bosonization of boundary vacuum state is realized by "monomial".
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