Many-body calculations of low-energy eigenstates in magnetic and periodic systems with self-healing diffusion Monte Carlo: steps beyond the fixed phase.
Many-body calculations of low-energy eigenstates in magnetic and periodic systems with self-healing diffusion Monte Carlo: steps beyond the fixed phase.
复制标题
具有自愈扩散蒙特卡罗的磁性和周期系统中低能本征态的多体计算：超越固定相位的步骤。
DOI：
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发表时间：
2010
影响因子：
4.4
通讯作者：
F. Reboredo
中科院分区：
文献类型：
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作者：
F. Reboredo
自愈扩散蒙特卡罗算法（SHDMC）[F. a.雷博雷多河Q. Hood和P.R. C.肯特，物理评论B 79，195117（2009）; F. a. Reboredo，同上，80，125110（2009）]被扩展到研究磁和周期系统的基态和激发态。当波函数足够灵活时，随着所收集的统计数据的增加，该方法收敛到精确的本征态。结果表明，节面的维数取决于相位是否为标量函数。一个递归的优化算法是从时间演化的混合概率密度，这是由一个合奏的电子配置（步行者）与复杂的重量。该复数权重允许固定节点波函数的相位远离试验波函数相位。这种新方法既是SHDMC的推广，也是固定相位近似[G。Ortiz，D. M. Ceperley和R. M. Martin，Phys Rev. Lett. 71，2777（1993）]。当递归使用时，它同时改善了节点和相位。该算法被证明收敛到模型系统的周期性边界条件或施加磁场的近精确解。计算成本与相位的独立自由度的数量成正比。该方法被应用于获得低能激发的哈密顿磁场。周期性的边界条件也被认为是优化波函数与扭曲的边界条件，其中包括在一个多体布洛赫相位。这种新的方法来研究周期，磁，和复杂的哈密顿的潜在应用进行了讨论。
The self-healing diffusion Monte Carlo algorithm (SHDMC) [F. A. Reboredo, R. Q. Hood, and P. R. C. Kent, Phys. Rev. B 79, 195117 (2009); F. A. Reboredo, ibid. 80, 125110 (2009)] is extended to study the ground and excited states of magnetic and periodic systems. The method converges to exact eigenstates as the statistical data collected increase if the wave function is sufficiently flexible. It is shown that the dimensionality of the nodal surface is dependent on whether phase is a scalar function or not. A recursive optimization algorithm is derived from the time evolution of the mixed probability density, which is given by an ensemble of electronic configurations (walkers) with complex weight. This complex weight allows the phase of the fixed-node wave function to move away from the trial wave function phase. This novel approach is both a generalization of SHDMC and the fixed-phase approximation [G. Ortiz, D. M. Ceperley, and R. M. Martin, Phys Rev. Lett. 71, 2777 (1993)]. When used recursively it simultaneously improves the node and the phase. The algorithm is demonstrated to converge to nearly exact solutions of model systems with periodic boundary conditions or applied magnetic fields. The computational cost is proportional to the number of independent degrees of freedom of the phase. The method is applied to obtain low-energy excitations of Hamiltonians with magnetic field. Periodic boundary conditions are also considered optimizing wave functions with twisted boundary conditions which are included in a many-body Bloch phase. The potential applications of this new method to study periodic, magnetic, and complex Hamiltonians are discussed.