Abstract ComBethAns is a Maple module developed to enable calculations concerning spin systems using combinatorial Bethe Ansatz approach. This method of spin system analysis is based on representation theory and combinatorics. It allows us to consider one-dimensional spin systems with periodic boundary conditions. The module ComBethAns offers tools to define the different bases for such quantum system, to carry out transformation between these bases and to reveal some important aspects of the quantum system. Particularly powerful features are the possibility to generate the Schur–Weyl transform and to quasi-diagonalize the Hamiltonian using projection method. Program summary Program Title: ComBethAns (Combinatorial Bethe Ansatz) CPC Library link to program files: http://dx.doi.org/10.17632/hkzw252dd5.1 Licensing provisions: MIT Programming language: Maple Nature of problem: Combinatorial Bethe Ansatz represents an approach to the solution of one-dimensional spin systems in terms of tools which are being applied in representation theory and combinatorics. In this approach one can distinguish some objects and operations which are exploited by different researchers. Here we want to define and make appropriate computer implementations of these basic objects and operations which will help researchers to deal with the spin systems. Solution method: The procedures being presented are based on the Schur–Weyl duality and the Robinson-Schensted-Knuth combinatorial algorithm. Such an approach allows to build different representations of the spin systems and to construct objects and operators which are essential in spin systems in a natural way. We also present a set of procedures which enable to determine energy values of such systems based on the use of bases adapted to the translational symmetry. Additional comments including restrictions and unusual features: We restrict ourselves to the systems consisting of 1 ∕ 2 spins, but many procedures may be applied for systems with greater spins.

中文翻译：

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用于 Bethe Ansatz 组合方面的 Maple 包

摘要 ComBethAns 是一个 Maple 模块，用于使用组合 Bethe Ansatz 方法进行有关自旋系统的计算。这种自旋系统分析方法基于表示理论和组合学。它允许我们考虑具有周期性边界条件的一维自旋系统。ComBethAns 模块提供了工具来定义这种量子系统的不同基础，在这些基础之间进行转换并揭示量子系统的一些重要方面。特别强大的功能是可以生成 Schur-Weyl 变换并使用投影方法对哈密顿量进行准对角化。程序概要 程序名称：ComBethAns (Combinatorial Bethe Ansatz) CPC 库程序文件链接：http://dx.doi.org/10.17632/hkzw252dd5.1 许可条款：麻省理工学院编程语言：Maple 问题性质：组合 Bethe Ansatz 代表了一种解决一维自旋系统的方法，这些工具正在应用于表示论和组合学中。在这种方法中，人们可以区分不同研究人员利用的一些对象和操作。在这里，我们希望定义这些基本对象和操作的适当计算机实现，这将有助于研究人员处理自旋系统。求解方法：所提出的程序基于 Schur-Weyl 对偶性和 Robinson-Schensted-Knuth 组合算法。这种方法允许构建自旋系统的不同表示，并以自然的方式构建自旋系统中必不可少的对象和运算符。我们还提出了一组程序，这些程序能够根据适用于平移对称性的基的使用来确定此类系统的能量值。包括限制和不寻常特征在内的其他评论：我们将自己限制在由 1 ∕ 2 自旋组成的系统中，但许多程序可能适用于具有更大自旋的系统。