Many-body calculations of low-energy eigenstates in magnetic and periodic systems with self-healing diffusion Monte Carlo: steps beyond the fixed-phase
Fernando Agustín Reboredo
备注：
Important correction due to a timely comment of a referee: The nodal structure of anti-symmetric eigenstates has nodes if the phase is a scalar function but may only have nodes at the coincidental points otherwise
自愈扩散蒙特卡罗算法（SHDMC）[Reboredo，Hood和Kent，Phys. Rev. B { \bf 79}，195117（2009）; Reboredo，{ \it ibid.} { \bf 80}，125110（2009）]扩展到研究磁性和周期性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。研究表明，反对称复本征态的波函数可以表示为反对称实因子和对称相因子的乘积。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振幅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[Ortiz，Ceperley和Martin，Phys Rev. Lett. { \bf 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比例。该方法适用于获得低能量激发的哈密顿与磁场或周期性的边界条件。该方法被用来优化波函数与扭曲的边界条件，这是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。
英文摘要：
The self-healing diffusion Monte Carlo algorithm (SHDMC) [Reboredo, Hood and Kent, Phys. Rev. B {\bf 79}, 195117 (2009); Reboredo, {\it ibid.} {\bf 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 increases if the wave function is sufficiently flexible. It is shown that the wave functions of complex anti-symmetric eigen-states can be written as the product of an anti-symmetric real factor and a symmetric phase factor. 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 amplitude 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 [Ortiz, Ceperley and Martin, Phys Rev. Lett. {\bf 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 or periodic boundary conditions. The method is used to optimize 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.
我们通常期望量子系统热化并满足本征态热化假设（ETH），该假设指出有限的能量密度本征态是热的。然而，一些系统，如多体局域系统和具有量子多体疤痕的系统，违反ETH并具有高能无热本征态。在有疤痕的系统中，大多数本征态热化，但少数非典型疤痕态不会。当特定的初始产物态随时间演化时，疤痕态可以引起周期性的复苏，这可以通过实验检测到。最近，发现了具有磁有序的3色本征态的自旋哈密顿算子族，这些本征态是量子多体伤疤[Lee et al. Phys. Rev. B 101，241111（2020）]。这些模型可以在任何可以用三角形平铺的晶格中实现，例如三角形或kagome晶格，并且已经被证明与海森堡kagome反铁磁体中的量子自旋液体物理学有密切联系。在这项工作中，我们介绍了一个广义家庭的$n$ -彩色哈密顿与“螺旋色”的本征态由$n$ -自旋图案，如多边形或多面体。我们展示了这些模型如何在许多不同的晶格几何形状中实现，并提供了数值证据，证明它们可以表现出量子多体疤痕，这些疤痕可以通过随时间演化的简单乘积态观察到。这些哈密顿量的简单结构使它们成为未来量子多体伤疤实验研究的有希望的候选者。
Density-Matrix Renormalization Group study of Many-Body Localization in Floquet Eigenstates
我们推广了最近引入的密度矩阵重整化群（DMRG-X）[Khemani et al，PRL 2016]算法，以获得一维周期驱动多体局域系统的Floquet本征态。这种推广是可能的事实，即时间演化算子的一个时期可以有效地表示使用矩阵乘积算子。我们首先基准的方法相比，精确对角化的小系统。然后，我们获得Floquet本征态较大的系统，并明确表明，特征面积律缩放仍然强大。
Periodic orbits and quantum many-body scars in integrable spin chains
Institute of Science and Technology Austria (ISTA)（奥地利科学技术研究所）；Technical University of Munich（慕尼黑工业大学）；Munich Center for Quantum Science and Technology (MCQST)（慕尼黑量子科学与技术中心）
