论文标题
机器学习量子状态 - 向费米昂 - 玻色子耦合系统的扩展和激发状态计算
Machine Learning Quantum States -- Extensions to Fermion-Boson Coupled Systems and Excited-State Calculations
论文作者
论文摘要
最近，为了分析量子多体汉密尔顿人，机器学习技术已被证明非常有用和有力。但是，此类机器学习求解器的适用性仍然有限。在这里，我们提出的方案使得可以应用机器学习技术来分析费米昂 - 玻色子耦合的汉密尔顿人并计算激发状态。至于Fermion-Boson耦合系统的扩展，我们研究了荷斯坦模型，作为费米昂 - 波森耦合汉密尔顿人的代表。我们表明，机器学习求解器可实现高度精确的地面能量，与通过变异蒙特卡洛方法获得的求解相比，其准确性大大提高了准确性。至于激发态的计算，我们提出了一种与K. Choo等人（物理）中提出的方法不同的方法。莱特牧师。 121（2018）167204。我们讨论了详细的差异，并使用一维$ s = 1/2 $ heisenberg链进行了两种方法的准确性。我们还显示了沮丧的二维$ s = 1/2 $ $ j_1 $ - $ J_2 $ HEISENBERG型号的基准，并与精确的对角线化获得的结果达成了极好的协议。这里显示的扩展名开了一种使用机器学习技术分析一般量子多体问题的方法。
To analyze quantum many-body Hamiltonians, recently, machine learning techniques have been shown to be quite useful and powerful. However, the applicability of such machine learning solvers is still limited. Here, we propose schemes that make it possible to apply machine learning techniques to analyze fermion-boson coupled Hamiltonians and to calculate excited states. As for the extension to fermion-boson coupled systems, we study the Holstein model as a representative of the fermion-boson coupled Hamiltonians. We show that the machine-learning solver achieves highly accurate ground-state energy, improving the accuracy substantially compared to that obtained by the variational Monte Carlo method. As for the calculations of excited states, we propose a different approach than that proposed in K. Choo et al., Phys. Rev. Lett. 121 (2018) 167204. We discuss the difference in detail and compare the accuracy of two methods using the one-dimensional $S=1/2$ Heisenberg chain. We also show the benchmark for the frustrated two-dimensional $S=1/2$ $J_1$-$J_2$ Heisenberg model and show an excellent agreement with the results obtained by the exact diagonalization. The extensions shown here open a way to analyze general quantum many-body problems using machine learning techniques.
