Hamiltonian reconstruction as metric for variational studies
Hamiltonian reconstruction as metric for variational studies
复制标题
DOI：
10.21468/scipostphys.13.3.063
复制
发表时间：
2021-01
期刊：
影响因子：
5.5
通讯作者：
Kevin Zhang;S. Lederer;Kenny Choo;T. Neupert;Giuseppe Carleo;Eun-Ah Kim
中科院分区：
文献类型：
--
作者：
Kevin Zhang;S. Lederer;Kenny Choo;T. Neupert;Giuseppe Carleo;Eun-Ah Kim
变分方法是近似求解量子多体问题的最有力的方法之一。这些包括基于张量或神经网络的变分状态，以及变分量子本征解算器中的参数化量子电路。然而，变分波函数的质量的自洽评价是一个众所周知的艰巨任务。使用最近开发的哈密顿重建方法，我们提出了一个多方面的方法来评估基于神经网络的波函数的质量。具体来说，我们考虑卷积神经网络（CNN）和受限玻尔兹曼机（RBM）状态，它们在正方形晶格自旋1/21/2J_1\！-\！J_2J1−J2海森堡模型我们发现，重建的哈密顿量通常是较少的挫折，并具有易轴各向异性附近的高挫折点。此外，重构的哈密顿量抑制了大J_2J_2极限下的量子涨落。我们的结果突出了波函数对称性的重要性。此外，从哈密顿重构的多方面的见解表明，变分波函数可能无法通过抑制量子涨落来捕获真正的基态。
Variational approaches are among the most powerful techniques to approximately solve quantum many-body problems. These encompass both variational states based on tensor or neural networks, and parameterized quantum circuits in variational quantum eigensolvers. However, self-consistent evaluation of the quality of variational wavefunctions is a notoriously hard task. Using a recently developed Hamiltonian reconstruction method, we propose a multi-faceted approach to evaluating the quality of neural-network based wavefunctions. Specifically, we consider convolutional neural network (CNN) and restricted Boltzmann machine (RBM) states trained on a square lattice spin-1/21/2J_1\!-\!J_2J1−J2 Heisenberg model. We find that the reconstructed Hamiltonians are typically less frustrated, and have easy-axis anisotropy near the high frustration point. In addition, the reconstructed Hamiltonians suppress quantum fluctuations in the large J_2J2 limit. Our results highlight the critical importance of the wavefunction’s symmetry. Moreover, the multi-faceted insight from the Hamiltonian reconstruction reveals that a variational wave function can fail to capture the true ground state through suppression of quantum fluctuations.