论文标题
发现使用费米子神经网络的量子相变
Discovering Quantum Phase Transitions with Fermionic Neural Networks
论文作者
论文摘要
深度神经网络非常成功，因为高度准确的波函数Ansätze用于分子基态的变异蒙特卡洛计算。我们将这种Ansatz，Ferminet的扩展为定期汉密尔顿人的基础状态，并研究同质电子气体。小型电子气体系统的基础能量的FERMINET计算与先前的启动器完全配置相互作用量子蒙特卡洛和扩散蒙特卡洛计算非常吻合。我们研究了自旋偏振的均质电子气体，并证明相同的神经网络结构能够准确地代表离域的费米液态和局部的Wigner晶体状态。该网络没有\ emph {先验}知道存在相变的知识，但是在高密度下以翻译不变的基态收敛，并自发地破坏对称性以在低密度下产生结晶基态。
Deep neural networks have been extremely successful as highly accurate wave function ansätze for variational Monte Carlo calculations of molecular ground states. We present an extension of one such ansatz, FermiNet, to calculations of the ground states of periodic Hamiltonians, and study the homogeneous electron gas. FermiNet calculations of the ground-state energies of small electron gas systems are in excellent agreement with previous initiator full configuration interaction quantum Monte Carlo and diffusion Monte Carlo calculations. We investigate the spin-polarized homogeneous electron gas and demonstrate that the same neural network architecture is capable of accurately representing both the delocalized Fermi liquid state and the localized Wigner crystal state. The network is given no \emph{a priori} knowledge that a phase transition exists, but converges on the translationally invariant ground state at high density and spontaneously breaks the symmetry to produce the crystalline ground state at low density.
