Luo Di, Clark Bryan K
Institute for Condensed Matter Theory and Department of Physics, University of Illinois at Urbana-Champaign, Illinois 61801, USA.
Phys Rev Lett. 2019 Jun 7;122(22):226401. doi: 10.1103/PhysRevLett.122.226401.
Obtaining an accurate ground state wave function is one of the great challenges in the quantum many-body problem. In this Letter, we propose a new class of wave functions, neural network backflow (NNB). The backflow approach, pioneered originally by Feynman and Cohen [Phys. Rev. 102, 1189 (1956)10.1103/PhysRev.102.1189], adds correlation to a mean-field ground state by transforming the single-particle orbitals in a configuration-dependent way. NNB uses a feed-forward neural network to learn the optimal transformation via variational Monte Carlo calculations. NNB directly dresses a mean-field state, can be systematically improved, and directly alters the sign structure of the wave function. It generalizes the standard backflow [L. F. Tocchio et al., Phys. Rev. B 78, 041101(R) (2008)10.1103/PhysRevB.78.041101], which we show how to explicitly represent as a NNB. We benchmark the NNB on Hubbard models at intermediate doping, finding that it significantly decreases the relative error, restores the symmetry of both observables and single-particle orbitals, and decreases the double-occupancy density. Finally, we illustrate interesting patterns in the weights and bias of the optimized neural network.
获得精确的基态波函数是量子多体问题中的重大挑战之一。在本快报中，我们提出了一类新的波函数——神经网络回流（NNB）。回流方法最初由费曼和科恩开创[《物理评论》102, 1189 (1956)10.1103/PhysRev.102.1189]，通过以依赖于组态的方式变换单粒子轨道，将关联添加到平均场基态中。NNB使用前馈神经网络通过变分蒙特卡罗计算来学习最优变换。NNB直接修饰平均场态，可以系统地改进，并且直接改变波函数的符号结构。它推广了标准回流[L. F. 托基奥等人，《物理评论B》78, 041101(R) (2008)10.1103/PhysRevB.78.041101]，我们展示了如何将其明确表示为一个NNB。我们在中等掺杂的哈伯德模型上对NNB进行基准测试，发现它显著降低了相对误差，恢复了可观测量和单粒子轨道的对称性，并降低了双占据密度。最后，我们展示了优化神经网络的权重和偏差中有趣的模式。
