高斯量子蒙特卡罗的系统误差及对称投影方法的系统研究
Systematic errors in Gaussian Quantum Monte Carlo and a systematic study of the symmetry projection method
摘要：
高斯量子蒙特卡罗（GQMC）是一种研究正权费米子的随机相空间方法。在哈伯德模型的例子中，接近一半的填充，它未能再现基态的所有对称性，导致低温下的系统误差。在以前的工作[Phys. Rev. B { \bf 72}，224518（2005）]中，我们提出通过将从模拟获得的密度矩阵投影到基态对称扇区上来恢复破坏的对称性。对于基态性质，该方法的精度取决于GQMC和精确密度矩阵之间的{ \it大重叠}。因此，该方法不是严格精确的。我们提出的方法的限制，通过系统的研究方法为2和3腿哈伯德阶梯不同的填充物和现场排斥强度。我们显示了几个迹象表明，系统误差源于非零边界项的部分积分步骤中的福克-普朗克方程的推导。检查尖峰轨迹和缓慢衰减的概率分布提供了一个重要的测试结果的可靠性。讨论了避免边界项的可能解决方案。此外，我们比较了两种不同的采样方法：步行者的重构和大都市算法得到的结果。
英文摘要：
Gaussian Quantum Monte Carlo (GQMC) is a stochastic phase space method for fermions with positive weights. In the example of the Hubbard model close to half filling it fails to reproduce all the symmetries of the ground state leading to systematic errors at low temperatures. In a previous work [Phys. Rev. B {\bf 72}, 224518 (2005)] we proposed to restore the broken symmetries by projecting the density matrix obtained from the simulation onto the ground state symmetry sector. For ground state properties, the accuracy of this method depends on a {\it large overlap} between the GQMC and exact density matrices. Thus, the method is not rigorously exact. We present the limits of the approach by a systematic study of the method for 2 and 3 leg Hubbard ladders for different fillings and on-site repulsion strengths. We show several indications that the systematic errors stem from non-vanishing boundary terms in the partial integration step in the derivation of the Fokker-Planck equation. Checking for spiking trajectories and slow decaying probability distributions provides an important test of the reliability of the results. Possible solutions to avoid boundary terms are discussed. Furthermore we compare results obtained from two different sampling methods: Reconfiguration of walkers and the Metropolis algorithm.
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