坐标系Bethe Answer的拼接与合并
Anchoring and Binning the Coordinate Bethe Ansatz
摘要：
坐标贝特安托（CBA）表示，作为一个排列之和，XXX海森堡自旋链哈密顿本征态的矩阵元素与一个国家与固定的自旋。这些矩阵元包括哈密顿本征态的波函数。然而，由于和的复杂性随着自旋链的长度N而迅速增长，因此连续极限中的精确波函数太麻烦而不能利用。在本文中，我们提供了一个近似的CBA的复杂性不直接依赖于N。这包括两个步骤。首先，我们在CBA中的指数参数中添加一个锚。锚是2 π的置换相关整数倍。一旦锚定，这些参数的分布简化，成为近似高斯分布。波函数由该分布的傅里叶变换给出，因此波函数的计算简化为分布的矩的计算。其次，我们将置换群参数化为整数之间的映射，并将这些映射装箱。然后，矩的计算简化为关于划分成箱的组合练习。作为一个例子，我们考虑的经典和量子基态之间的矩阵元。
英文摘要：
The Coordinate Bethe Ansatz (CBA) expresses, as a sum over permutations, the matrix element of an XXX Heisenberg spin chain Hamiltonian eigenstate with a state with fixed spins. These matrix elements comprise the wave functions of the Hamiltonian eigenstates. However, as the complexity of the sum grows rapidly with the length N of the spin chain, the exact wave function in the continuum limit is too cumbersome to be exploited. In this note we provide an approximation to the CBA whose complexity does not directly depend upon N. This consists of two steps. First, we add an anchor to the argument of the exponential in the CBA. The anchor is a permutation-dependent integral multiple of 2 pi. Once anchored, the distribution of these arguments simplifies, becoming approximately Gaussian. The wave function is given by the Fourier transform of this distribution and so the calculation of the wave function reduces to the calculation of the moments of the distribution. Second, we parametrize the permutation group as a map between integers and we bin these maps. The calculation of the moments then reduces to a combinatorial exercise on the partitioning into bins. As an example we consider the matrix element between the classical and quantum ground states.
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。
