发表机构
Laboratoire de Chimie et Physique Quantiques (UMR 5626), CNRS and Université de Toulouse（量子化学与物理实验室（联合研究单位5626），法国国家科学研究中心和图卢兹大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文将自修复扩散蒙特卡洛（SHDMC）应用于一维费米子模型，发现其标准形式会收敛至错误节点，修改节点更新准则可部分解决问题，一般情形收敛或需局域基组。
AI 中文摘要
我们采用具有周期性边界条件的一维模型对自修复扩散蒙特卡洛（SHDMC）方法展开研究。引入反演对称性以模拟费米子波函数的反对称属性，其中玻色子部分和费米子部分分别由偶宇称和奇宇称本征态建模。与实际费米子系统类似，该模型的节点结构仅被对称性部分约束，因此成为SHDMC这类节点优化算法的非平凡测试平台。我们表明，SHDMC迭代下的节点演化可被转化为兼具吸引和排斥不动点的动力系统。在将标准SHDMC形式应用于该模型时，发现固定节点能量会随迭代升高，且节点收敛至错误值，这表明SHDMC并不总能收敛到正确解。我们进一步表明，通过修改节点更新准则以更重视节点区域，该问题可被部分解决。在一般情形下实现收敛很可能需要使用局域基组，本模型即属此类情况。
英文摘要
We investigate the Self-Healing Diffusion Monte Carlo (SHDMC) method using a one-dimensional model with periodic boundary conditions. An inversion symmetry is introduced to mimic the antisymmetry property of fermionic wave functions, with the bosonic and fermionic sectors being modeled by the even and odd eigenstates, respectively. As in realistic fermionic systems, the nodal structure is only partially constrained by symmetry, making this model a non-trivial testbed for nodal optimization algorithms such as SHDMC. We show that the nodal evolution under SHDMC iterations can be cast into a dynamical system exhibiting both attractive and repulsive fixed points. When applying SHDMC to this model in the absence of statistical noise, the fixed-node energy is found to increase during iterations and the node converges to an incorrect value. This occurs for any finite basis, even when the exact node is representable in it; the attractive fixed point approaches the exact node only as the basis becomes complete, while the convergence toward it becomes increasingly slow. We further show that this problem can be largely cured by modifying the nodal update criterion to give more importance to the nodal region. Our results suggest that, in the general case, an efficient nodal optimization may require both an improved nodal update criterion and a localized basis set allowing local distortions of the trial wave function, as is the case for this model.
Comments12 pages, 11 figures
