kagome格子上吸引Hubbard模型的加速量子蒙特卡罗模拟
Accelerated quantum Monte Carlo simulations of the attractive Hubbard model on the kagome lattice
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中文总结 AI 辅助
本文结合FFT与延迟更新算法加速DQMC模拟，实现kagome格子吸引Hubbard模型的大尺寸仿真，揭示狄拉克填充处零温超流量子临界性，证实三角规则电荷密度波序为有限尺寸效应，计算成本标度优于传统DQMC。
中文摘要 AI 辅助
近期数类kagome材料的发现以及光学kagome格子的实验实现，激发了对kagome格子上相互作用驱动的关联态的数值研究。在现有数值方法中，行列式量子蒙特卡罗（DQMC）是研究这类强关联态的有力工具，但现有DQMC模拟可及的系统尺寸仍然有限，无法开展可靠的有限尺寸标度分析。本文中，我们开发了一种基于快速傅里叶变换（FFT）的通用加速方案，用于复合格子上的传播子乘法，并将其与延迟更新算法结合，实现了比以往DQMC研究大两倍的系统尺寸的模拟，从而能对吸引kagome格子Hubbard模型进行可靠的有限尺寸标度分析。我们的大规模模拟揭示了狄拉克填充处相互作用驱动的零温超流量子临界性，并给出了相关临界指数的可靠估计。此外，我们未发现先前提出的三角规则电荷密度波序在热力学极限下存在的证据，表明其很可能是有限尺寸效应。而且，对于当前二维光学格子实验可及的系统尺寸，FFT与延迟更新结合的方案表现出的有效计算成本标度为$N^{2.49}$，远低于传统DQMC模拟的$\boldsymbol{\text{O}}(N^3)$计算成本。
英文摘要
The recent discovery of several families of kagome materials and experimental realization of optical kagome lattices have stimulated growing numerical studies of interaction-driven correlated states on the kagome lattice. Among the available numerical approaches, determinant quantum Monte Carlo (DQMC) is a powerful method for investigating such strongly correlated states. However, the accessible system sizes of existing DQMC simulations remain limited, preventing reliable finite-size scaling analyses. Here we develop a general acceleration scheme based on fast Fourier transform (FFT) for propagator multiplications on composite lattices and combine it with the delay-update algorithm, enabling simulations on system sizes twice as large as those of previous DQMC studies, allowing reliable finite-size scaling analyses of the attractive kagome-lattice Hubbard model. Our large-scale simulations reveal the interaction-driven zero-temperature superfluid quantum criticality at the Dirac filling and provide reliable estimates of the associated critical exponents. Besides, we find no evidence that the previously proposed triangle-rule charge-density-wave order survives in the thermodynamic limit, suggesting that it is likely a finite-size effect. Moreover, for system sizes accessible in current two-dimensional optical lattice experiments, the combined FFT and delay-update scheme exhibits an effective computational cost scaling as $N^{2.49}$, substantially below the $\mathcal{O}(N^3)$ computational cost of conventional DQMC simulations.
