多体问题中符号误差的系统减少：自愈扩散蒙特卡罗推广到激发态
Systematic reduction of sign errors in many-body problems: generalization of self-healing diffusion Monte Carlo to excited states
摘要：
最近发展的自愈扩散蒙特卡罗算法[PRB 79，195117]扩展到激发态的计算。形式主义是基于激发态固定节点近似和混合估计的激发态概率密度。用递归方法同时求出了不等价节袋的固定节基态波函数。使用两种方法防止波函数衰减到较低能量状态：i）去除改进的试探波函数到先前计算的本征态的投影。ii）调整每个节点袋的参考能量，以便在全局固定节点波函数中产生扭结，当局部平滑时，以较低能量袋为代价增加较高能量袋的体积，直到每个袋的能量变得相等。这种参考能量方法的目的是找到节点结构，是一个给定的节点拓扑结构内的节点的任意波动的局部最小值。我们证明了在一个模型系统中，该算法收敛到玻色子和费米子的情况下的多体本征态。
英文摘要：
A recently developed self-healing diffusion Monte Carlo algorithm [PRB 79, 195117] is extended to the calculation of excited states. The formalism is based on an excited-state fixed-node approximation and the mixed estimator of the excited-state probability density. The fixed-node ground state wave-functions of inequivalent nodal pockets are found simultaneously using a recursive approach. The decay of the wave-function into lower energy states is prevented using two methods: i) The projection of the improved trial-wave function into previously calculated eigenstates is removed. ii) The reference energy for each nodal pocket is adjusted in order to create a kink in the global fixed-node wave-function which, when locally smoothed out, increases the volume of the higher energy pockets at the expense of the lower energy ones until the energies of every pocket become equal. This reference energy method is designed to find nodal structures that are local minima for arbitrary fluctuations of the nodes within a given nodal topology. We demonstrate in a model system that the algorithm converges to many-body eigenstates in bosonic-like and fermionic cases.
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