Nonlinear biases, stochastically sampled effective Hamiltonians, and spectral functions in quantum Monte Carlo methods
Nonlinear biases, stochastically sampled effective Hamiltonians, and spectral functions in quantum Monte Carlo methods
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DOI：
10.1103/physrevb.98.085118
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发表时间：
2018-08-09
影响因子：
3.7
通讯作者：
Booth, George H.
中科院分区：
文献类型：
--
作者：
Blunt, Nick S.;Alavi, Ali;Booth, George H.
在这篇文章中，我们研究了量子蒙特卡罗方法中由于非线性期望值的积累而可能出现的系统偏差的例子，以及纠正这些误差的方法。我们从Krylov投影的全组态相互作用量子蒙特卡罗方法(KP-FCIQMC)开始研究，该方法最近被引入以允许高效、随机地计算动力学性质。这需要一个采样的有效哈密顿量的解，从而导致对这些随机变量的非线性运算。我们研究了这个特征值问题的概率分布，以研究该方法中的随机误差和系统偏差，并证明了这种误差可以通过移动到更合适的基来显著地校正。最后扩展到考虑Ceperley和Bernu的关联函数量子蒙特卡罗(QMC)方法，展示了如何在全组态相互作用QMC(FCIQMC)框架中采用这种方法。
In this paper, we study examples of systematic biases that can occur in quantum Monte Carlo methods due to the accumulation of nonlinear expectation values, and approaches by which these errors can be corrected. We begin with a study of the Krylov-projected full configuration interaction quantum Monte Carlo (KP-FCIQMC) approach, which was recently introduced to allow efficient, stochastic calculation of dynamical properties. This requires the solution of a sampled effective Hamiltonian, resulting in a nonlinear operation on these stochastic variables. We investigate the probability distribution of this eigenvalue problem to study both stochastic errors and systematic biases in the approach, and demonstrate that such errors can be significantly corrected by moving to a more appropriate basis. This is lastly expanded to include consideration of the correlation function quantum Monte Carlo (QMC) approach of Ceperley and Bernu, showing how such an approach can be taken in the full configuration interaction QMC (FCIQMC) framework.