We study a continuum model of the interface of charge neutral graphene and vacuum in the quantum Hall regime via a sign-problem-free quantum Monte Carlo, allowing us to investigate the interplay of topology and strong interactions in a graphene quantum Hall edge for large system sizes. We focus on the topological phase transition from the spin-polarized state with symmetry-protected gapless helical edges to the fully charge gapped canted-antiferromagnet state with spontaneous symmetry breaking, driven by the Zeeman energy. Our large system size simulations allow us to detail the behavior of various quantities across this transition that are amenable to being probed experimentally, such as the spatially and energy-resolved local density of states and the local compressibility. We find peculiar kinks in the branches of the edge dispersion, and also an unexpectedly large charge susceptibility in the bulk of the canted antiferromagnet associated with its Goldstone mode.

中文翻译：

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石墨烯量子霍尔边缘的量子蒙特卡罗

我们通过无符号问题的量子蒙特卡洛研究了量子霍尔区域中电荷中性石墨烯和真空界面的连续体模型，使我们能够研究大型系统的石墨烯量子霍尔边缘中拓扑结构和强相互作用的相互作用尺寸。我们专注于从具有对称保护的无间隙螺旋边缘的自旋极化状态到由塞曼能量驱动的具有自发对称破坏的完全电荷间隙倾斜反铁磁状态的拓扑相变。我们的大型系统尺寸模拟使我们能够详细说明在这个过渡过程中各种量的行为，这些量可以通过实验进行探测，例如空间和能量分辨的局部状态密度和局部可压缩性。我们在边缘分散的分支中发现了特殊的扭结，