基于混合蒙特卡罗模拟的非阿贝尔分数量子霍尔效应中的任意子编织
Many-Anyon Braiding in Non-Abelian Fractional Quantum Hall Effect with Hybrid Monte Carlo Simulation
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中文总结 AI 辅助
该研究采用混合蒙特卡罗方法，发现基于全局旋转的任意子编织方案对有限尺寸效应鲁棒，探究了电子相互作用和局域势对融合通道的影响，结果对非阿贝尔物理实验实现有重要意义。
中文摘要 AI 辅助
我们采用混合蒙特卡罗方法，高效计算与Moore-Read准空穴不同编织方案相关的多任意子非阿贝尔编织矩阵。本工作的一项新发现是，基于全局旋转的任意子编织方案对有限尺寸效应具有鲁棒性，这通过将其编织矩阵误差与简单的两任意子交换的误差进行基准测试得到了证明。此外，我们研究了电子-电子相互作用和局域静电俘获势如何影响不同融合通道的能量偏好，及其对非阿贝尔编织矩阵的影响已得到验证，这一令人惊讶的现象展现了非阿贝尔态的长程纠缠。我们的结果与分数量子霍尔效应及其他类似系统中非阿贝尔物理的实验实现相关，包括快速发展的莫尔材料中的分数量子反常霍尔态领域。
英文摘要
We employ the hybrid Monte Carlo method to efficiently compute the many-anyon non-Abelian braiding matrices associated with different braiding schemes of the Moore-Read quasiholes. A novel proposal in this work is that anyon braiding schemes based on a global rotation are robust against finite-size effects, as demonstrated by benchmarking their errors in the braiding matrix against those of a simple two-anyon exchange. Moreover, we investigate how electron-electron interactions and local electrostatic trapping potentials influence the energetic preference of different fusion channels. Their effect on the non-Abelian braiding matrices has been verified, a surprising phenomenon that demonstrates long-range entanglement of non-Abelian states. Our results are relevant to the experimental realization of non-Abelian physics in fractional quantum Hall and other analogous systems, including the fast-growing field of fractional quantum anomalous Hall states in moiré materials.
