格场论系统中基于算子子空间的高能级提取方法
Operator subspace based method for the extraction of higher energy levels in Lattice field theoretic systems
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中文总结 AI 辅助
针对格点量子场论的高激发态能级提取，提出基于算子子空间的算法，经简谐与非简谐振子的格点蒙特卡洛模拟验证，该方法提取中间激发态性能优于标准GEVP方法，但提取基态性能弱于GEVP方法。
中文摘要 AI 辅助
鉴于格点量子场论数据的谱分析具有重要意义，相关技术的发展至关重要。因此，我们提出一种算法，该算法利用关联函数矩阵的前三个时间片构造转移矩阵并提取其能量本征值。通过改变算子子空间的维度并应用本征值-外推法，可降低因截断算子基而产生的系统误差。由于早期时间片的关联函数通常具有较小的统计误差且保留了强激发态的信号，我们期望所提方法在提取高激发态能量时表现良好。本文中，我们对量子力学系统（简谐和非简谐振子）进行了两次格点蒙特卡洛模拟，以评估所提方法在提取高激发态能量时的效率。我们将使用标准GEVP方法与所提方法得到的能级进行比较，发现对于两种系统，所提方法在提取中间激发态时始终优于标准GEVP方法。由于所提方法仅能访问前三个时间片，以当前形式提取基态能量时，它不如GEVP方法适用。
英文摘要
Given the importance of spectral analysis of lattice quantum field theory data, the advancement of techniques for the same remains critically important. Therefore, we propose an algorithm that uses the first three time slices of the correlation function matrix to construct the transfer matrix and extract its energy eigenvalues. Reduction of systematic error arising from truncating the operator basis is achieved by varying the operator subspace dimension and applying eigenvalue-variance extrapolation. Since the correlation functions in early time slices typically exhibit small statistical errors and retain a strong signal of higher-excited states, we expect our proposed method to perform well in extracting higher-excited-state energies. In this paper, we conduct two lattice Monte Carlo simulations for quantum mechanical systems, harmonic and anharmonic oscillators, to evaluate the efficiency of our proposed method for higher-excited-state energies. We compare the energy levels obtained using the standard GEVP method and our proposed method. We find that our method consistently outperforms the standard GEVP method in extracting intermediate excited states for both systems. Because our method has access only to the first three time slices, it is not preferable to the GEVP method for extracting the ground-state energy in its current form.
