This paper is a manual with tips and tricks for programming tensor network algorithms with global $SU(2)$ symmetry. We focus on practical details that are many times overlooked when it comes to implementing the basic building blocks of codes, such as useful data structures to store the tensors, practical ways of manipulating them, and so forth. Here we do not restrict ourselves to any specific tensor network method, but keep always in mind that the implementation should scale well for simulations of higher-dimensional systems using, e.g., Projected Entangled Pair States, where tensors with many indices may show up. To this end, the structural tensors (or intertwiners) that arise in the usual decomposition of $SU(2)$-symmetric tensors are never explicitly stored throughout the simulation. Instead, we store and manipulate the corresponding fusion trees - an algebraic specification of the symmetry constraints on the tensor - in order to implement basic $SU(2)$-symmetric tensor operations.

中文翻译：

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具有全局 SU(2) 对称性的张量网络编程指南

这篇论文是一本手册，其中包含对具有全局 $SU(2)$ 对称性的张量网络算法进行编程的提示和技巧。我们专注于在实现代码的基本构建块时经常被忽视的实际细节，例如用于存储张量的有用数据结构、操作它们的实用方法等。在这里，我们不限制自己使用任何特定的张量网络方法，但请始终记住，对于使用例如投影纠缠对状态的高维系统的模拟，实现应该可以很好地扩展，其中可能会出现具有许多索引的张量。为此，在 $SU(2)$-对称张量的通常分解中出现的结构张量（或交织器）从未在整个模拟过程中明确存储。反而，