量子蒙特卡罗方法中的非线性偏差、随机采样有效哈密顿量和谱函数
Non-linear biases, stochastically-sampled effective Hamiltonians and spectral functions in quantum Monte Carlo methods
摘要：
在这篇文章中，我们研究的系统偏差，可能会发生在量子蒙特卡罗方法由于非线性期望值的积累，以及这些错误可以被纠正的方法的例子。我们首先研究的Krylov投影FCIQMC（KP-FCIQMC）的方法，这是最近推出的，允许有效的，随机计算的动力学性质。这需要采样的有效哈密顿量的解决方案，导致在这些随机变量上的非线性操作。我们调查这个特征值问题的概率分布，研究随机误差和系统偏差的方法，并证明，这种错误可以显着纠正移动到一个更合适的基础。这是最后扩展到包括考虑Ceperley和Bernu的关联函数QMC方法，显示如何在FCIQMC框架中采取这样的方法。
英文摘要：
In this article we study examples of systematic biases that can occur in quantum Monte Carlo methods due to the accumulation of non-linear expectation values, and approaches by which these errors can be corrected. We begin with a study of the Krylov-projected FCIQMC (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 non-linear 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 QMC approach of Ceperley and Bernu, showing how such an approach can be taken in the FCIQMC framework.
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