机器学习量子态--费米子-玻色子耦合系统的扩展和激发态计算
Machine Learning Quantum States -- Extensions to Fermion-Boson Coupled Systems and Excited-State Calculations
摘要：
为了分析量子多体哈密顿，最近，机器学习技术已经被证明是非常有用和强大的。然而，这种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，使之有可能应用机器学习技术来分析费米子-玻色子耦合哈密顿量和计算激发态。至于推广到费米子-玻色子耦合系统，我们研究了作为费米子-玻色子耦合哈密顿量代表的Holstein模型。我们表明，机器学习求解器实现了高度准确的基态能量，与变分蒙特卡罗方法相比，大大提高了精度。对于激发态的计算，我们提出了与K. Choo等人，物理修订版信函121（2018）167204.我们详细讨论了这两种方法的差异，并使用一维$S=1/2$海森堡链比较了两种方法的精度。我们还显示了基准的挫折二维$S=1/2$ $J_1$ - $J_2$海森堡模型，并显示出良好的协议所获得的结果的精确对角化。这里展示的扩展打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。
英文摘要：
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.
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