标题： 隐藏费米子行列式状态假设在不同复杂度度量下的效率 显示英文标题

标题： Efficiency of the hidden fermion determinant states Ansatz in the light of different complexity measures

摘要： 寻找量子多体问题的可靠近似是现代物理学的核心挑战之一。 这项努力的关键在于开发先进的数值技术，以突破可处理的极限。 一种最近提出的数值技术是神经量子态。 这种基于波函数的假设利用神经网络的表达能力来解决根本性的难题，例如莫特转变。 在本文中，我们旨在评估神经网络假设之一——隐藏费米子斯莱特行列式方法的普遍性。 为此，我们研究了五个不同的费米子模型，每个模型都表现出纠缠熵的体积定律尺度。 对于这些模型，我们将假设的有效性与不同的复杂度度量相关联。 每个度量表明，在缺乏该复杂度的情况下，传统假设会变得高效。 我们提供了证据，表明当其中一个度量表明接近传统方法可以可靠工作的参数区域时，神经网络方法也能够可靠且高效地工作。 这突显了神经网络方法的巨大潜力，但也带来了挑战：在理论空间中找到合适的点，围绕这些点构建假设，以便能够有效处理当前设计不适合的模型。 显示英文摘要

摘要： Finding reliable approximations to the quantum many-body problem is one of the central challenges of modern physics. Elemental to this endeavor is the development of advanced numerical techniques pushing the limits of what is tractable. One such recently proposed numerical technique are neural quantum states. This new type of wavefunction based Ans\"atze utilizes the expressivity of neural networks to tackle fundamentally challenging problems, such as the Mott transition. In this paper we aim to gauge the universalness of one representative of neural network Ans\"atze, the hidden-fermion slater determinant approach. To this end, we study five different fermionic models each displaying volume law scaling of the entanglement entropy. For these, we correlate the effectiveness of the Ansatz with different complexity measures. Each measure indicates a different complexity in the absence of which a conventional Ansatz becomes efficient. We provide evidence that whenever one of the measures indicates proximity to a parameter region in which a conventional approach would work reliable, the neural network approach also works reliable and efficient. This highlights the great potential, but also challenges for neural network approaches: Finding suitable points in theory space around which to construct the Ansatz in order to be able to efficiently treat models unsuitable for their current designs.