由Yang-Baxter方程的常数不可逆解得到的非厄米可积系统

IF 5.4 1区 物理与天体物理 Q1 Physics and Astronomy
Somnath Maity, Pramod Padmanabhan, Vladimir Korepin
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引用次数: 0

摘要

通过对常数不可逆Yang-Baxter解进行baxter化,构造了可逆谱参数相关的Yang-Baxter解(r -矩阵)。解是代数的(表示无关的)。它们是用超对称(SUSY)代数构造的。得到的r矩阵是正则的,从而得到用SUSY生成器表示的局部非厄米哈密顿量。作为一个特殊的例子,我们对Hietarinta的4 × 4常数不可逆解进行了化,得到了最近邻哈密顿量。通过与文献的比较,我们发现其中有两个模型是新的。除了是非厄密的,它们中的许多也具有有趣的谱,是不可对角化的。利用SUSY生成子的适当表示,我们得到了所有局部希尔伯特空间维上的自旋链。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Non-hermitian integrable systems from constant non-invertible solutions of the Yang-Baxter equation

We construct invertible spectral parameter dependent Yang-Baxter solutions (R-matrices) by Baxterizing constant non-invertible Yang-Baxter solutions. The solutions are algebraic (representation independent). They are constructed using supersymmetry (SUSY) algebras. The resulting R-matrices are regular leading to local non-hermitian Hamiltonians written in terms of the SUSY generators. As particular examples we Baxterize the 4 × 4 constant non-invertible solutions of Hietarinta leading to nearest-neighbor Hamiltonians. On comparing with the literature we find that two of the models are new. Apart from being non-hermitian, many of them are also non-diagonalizable with interesting spectrums. With appropriate representations of the SUSY generators we obtain spin chains in all local Hilbert space dimensions.

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来源期刊
Journal of High Energy Physics
Journal of High Energy Physics 物理-物理:粒子与场物理
CiteScore
10.30
自引率
46.30%
发文量
2107
审稿时长
1.5 months
期刊介绍: The aim of the Journal of High Energy Physics (JHEP) is to ensure fast and efficient online publication tools to the scientific community, while keeping that community in charge of every aspect of the peer-review and publication process in order to ensure the highest quality standards in the journal. Consequently, the Advisory and Editorial Boards, composed of distinguished, active scientists in the field, jointly establish with the Scientific Director the journal''s scientific policy and ensure the scientific quality of accepted articles. JHEP presently encompasses the following areas of theoretical and experimental physics: Collider Physics Underground and Large Array Physics Quantum Field Theory Gauge Field Theories Symmetries String and Brane Theory General Relativity and Gravitation Supersymmetry Mathematical Methods of Physics Mostly Solvable Models Astroparticles Statistical Field Theories Mostly Weak Interactions Mostly Strong Interactions Quantum Field Theory (phenomenology) Strings and Branes Phenomenological Aspects of Supersymmetry Mostly Strong Interactions (phenomenology).
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