arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 1902.04079cond-mat.str-elcond-mat.dis-nn
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无序交互系统中竞争序的多面机器学习

Multi-faceted machine learning of competing orders in disordered interacting systems

Michael Matty, Yi Zhang, Zlatko Papic, Eun-Ah Kim

摘要:

虽然分数量子霍尔机制中的非微扰相互作用效应可以通过精确对角化很容易地模拟,但建立一种合适的诊断方法来标记存在竞争相互作用和无序的不同阶段是具有挑战性的。在这里,我们介绍了一个多方面的框架,使用一个简单的人工神经网络(ANN)来检测定义功能的分数量子霍尔态,电荷密度波态和本地化的状态,使用纠缠光谱和电荷密度作为独立的输入。我们考虑了微扰相互作用($l = 1$赝势$ΔV_1$)、无序势$W$和库仑相互作用在填充分数$ν = 1/3$时对系统的竞争效应。我们的相图基准以及对以前的相边界的估计,使用传统的措施沿$ΔV_1 = 0$和$W = 0$轴,传统的方法已被探索的唯一地区。此外,探索整个二维相图的第一次,我们建立了分数量子霍尔态的鲁棒性和映射出的电荷密度波微乳液相,其中的电荷密度波区域的液滴出现之前的电荷密度波完全无序。因此,我们建立的人工神经网络可以访问和学习的定义特征的拓扑以及对称性破缺阶段使用多方面的输入纠缠谱和电荷密度。

英文摘要:

While the non-perturbative interaction effects in the fractional quantum Hall regime can be readily simulated through exact diagonalization, it has been challenging to establish a suitable diagnostic that can label different phases in the presence of competing interactions and disorder. Here we introduce a multi-faceted framework using a simple artificial neural network (ANN) to detect defining features of a fractional quantum Hall state, a charge density wave state and a localized state using the entanglement spectra and charge density as independent input. We consider the competing effects of a perturbing interaction ($l = 1$ pseudopotential $ΔV_1$), a disorder potential $W$, and the Coulomb interaction to the system at filling fraction $ν = 1/3$. Our phase diagram benchmarks well against previous estimates of the phase boundary using conventional measures along the $ΔV_1 = 0$ and $W = 0$ axes, the only regions where conventional approaches have been explored. Moreover, exploring the entire two-dimensional phase diagram for the first time, we establish the robustness of the fractional quantum Hall state and map out the charge density wave micro-emulsion phase wherein droplets of charge density wave region appear before the charge density wave is completely disordered. Hence we establish that the ANN can access and learn the defining traits of topological as well as broken symmetry phases using multi-faceted inputs of entanglement spectra and charge density.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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