标题： 确定性假设在网络波函数表达能力中的表达能力 显示英文标题

标题： Expressivity of determinantal anzatzes for neural network wave functions

摘要： 神经网络波函数在解决多体量子问题方面展现出了高精度的潜力。 这些波函数通常使用行列式或行列式的和来反对称化由神经网络描述的多体轨道。 在之前的文献中，自旋被当作非动力学变量处理，每个电子被赋予一个固定的自旋标签（向上或向下）。 这种处理方式适用于自旋无关算符；然而，它无法应用于自旋相关的物理问题，例如含有自旋-轨道相互作用的哈密顿量。 我们扩展了神经网络以处理完全旋量形式的波函数，这可以应用于自旋相关的物理问题。 我们还表明，对于自旋无关的哈密顿量，传统的Hartree-Fock类似行列式、完全旋量波函数以及Pfau等人提出的所谓完全行列式波函数之间存在严格的上限关系。 旋量波函数与完全行列式之间的联系源于完全行列式波函数是旋量波函数在固定自旋投影后的结果，在自旋无关的情况下隐含地恢复了反对称性。 对于自旋相关的哈密顿量，完全行列式波函数不适用，因为它不具备反对称性。 H$_3$分子和二维均匀电子气的数值实验验证了这些界限。 显示英文摘要

摘要： Neural network wave functions have shown promise as a way to achieve high accuracy on the many-body quantum problem. These wave functions most commonly use a determinant or sum of determinants to antisymmetrize many-body orbitals which are described by a neural network. In previous literature, the spin has been treated as a non-dynamical variable, with each electron assigned a fixed spin label of up or down. Such a treatment is allowed for spin-independent operators; however, it cannot be applied to spin-dependent problems, such as Hamiltonians containing spin-orbit interactions. We provide an extension of neural networks to fully spinor wave functions, which can be applied to spin-dependent problems. We also show that for spin-independent Hamiltonians, a strict upper bound property is obeyed between a traditional Hartree-Fock like determinant, full spinor wave function, and the so-called full determinant wave function of Pfau et al. The relationship between a spinor wave function and the full determinant arises because the full determinant wave function is the spinor wave function projected onto a fixed spin, after which antisymmetry is implicitly restored in the spin-independent case. For spin-dependent Hamiltonians, the full determinant wave function is not applicable, because it is not antisymmetric. Numerical experiments on the H$_3$ molecule and two-dimensional homogeneous electron gas confirm the bounds.