Laughlin波函数的超行列式计算
Hyperdeterminantal computation for the Laughlin wave function
摘要：
劳克林波函数在斯莱特正交基中的分解出现在关于劳克林态的二次量子化形式的讨论中，并且直接等价于范德蒙德行列式的偶次幂在舒尔基中的分解。这样的计算是出了名的困难，膨胀系数还没有得到解释。在本文中，我们给出了这些系数的稀疏张量的超行列式的表达式。我们使用这个结果来构建一个算法，允许计算一个系数的发展，而不计算其他的。多亏了{ \tt C}中的一个程序，我们对范德蒙的平方进行了计算，直到11个字母表。
英文摘要：
The decomposition of the Laughlin wave function in the Slater orthogonal basis appears in the discussion on the second-quantized form of the Laughlin states and is straightforwardly equivalent to the decomposition of the even powers of the Vandermonde determinants in the Schur basis. Such a computation is notoriously difficult and the coefficients of the expansion have not yet been interpreted. In our paper, we give an expression of these coefficients in terms of hyperdeterminants of sparse tensors. We use this result to construct an algorithm allowing to compute one coefficient of the development without computing the others. Thanks to a program in {\tt C}, we performed the calculation for the square of the Vandermonde up to an alphabet of eleven lettres.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
