Abstract

Systems of quantum spins \(1/2\) with isotropic Heisenberg interaction play an important role in physics. In studying such systems, it may be useful to have a complete, yet non-overcomplete, basis of operators each of which has the symmetry of the Hamiltonian, i.e., is invariant with respect to rotations (global \(\mathrm{SU}(2)\) transformations of the Pauli matrices). This paper presents an algorithm for constructing such a basis. The algorithm is implemented in Wolfram Mathematica.

中文翻译：

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在 $$N$$ 量子自旋 $$1/2$$ 的旋转不变算子空间的完全基础上

摘要

具有各向同性海森堡相互作用的量子自旋\(1/2\)系统在物理学中起着重要作用。在研究此类系统时，拥有一个完整但非过完备的算子基可能很有用，其中每个算子都具有哈密顿量的对称性，即相对于旋转是不变的（全局\(\mathrm{SU}( 2)\)泡利矩阵的变换）。本文提出了一种构建这种基的算法。该算法在 Wolfram Mathematica 中实现。