标题： FCI-QMC方法在费米极化子中的应用 显示英文标题

标题： FCI-QMC approach to the Fermi polaron

摘要： 使用量子蒙特卡罗方法寻找费米子哈密顿量的基态是一个非常困难的问题，这是由于费米子符号问题。 虽然仍然呈指数级增长，但全组态相互作用蒙特卡罗（FCI-QMC）通过允许噪声的湮灭来减轻一些指数方差——每当两个行走者以相反符号到达同一构型时，它们就会从模拟中移除。 尽管FCI-QMC在量子化学问题中取得了相当大的成功，但它在凝聚态系统问题中的应用却有限。 在本文中，我们将FCI-QMC应用于费米极化子问题，这为改进算法提供了一个理想的测试平台。 在最简单形式下，FCI-QMC对于甚至相对较小的系统尺寸都是不稳定的。 然而，通过一系列算法改进，我们能够显著提高其有效性。 我们将固定节点QMC修改为适用于这些系统，引入一个经过良好选择的重要采样试探波函数，部分节点近似以及释放节点的一种变体。 最后，我们开发了一种直接在热力学极限下进行FCI-QMC的方法。 显示英文摘要

摘要： Finding the ground state of a fermionic Hamiltonian using quantum Monte Carlo is a very difficult problem, due to the Fermi sign problem. While still scaling exponentially, full configuration-interaction Monte Carlo (FCI-QMC) mitigates some of the exponential variance by allowing annihilation of noise -- whenever two walkers arrive at the same configuration with opposite signs, they are removed from the simulation. While FCI-QMC has been quite successful for quantum chemistry problems, its application to problems in condensed systems has been limited. In this paper, we apply FCI-QMC to the Fermi polaron problem, which provides an ideal test-bed for improving the algorithm. In its simplest form, FCI-QMC is unstable for even a fairly small system sizes. However, with a series of algorithmic improvements, we are able to significantly increase its effectiveness. We modify fixed node QMC to work in these systems, introduce a well chosen importance sampled trial wave function, a partial node approximation, and a variant of released node. Finally, we develop a way to perform FCI-QMC directly in the thermodynamic limit.