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Interaction-induced anomalous quantum Hall state on the honeycomb lattice

机译：相互作用引起的蜂窝格上的异常量子霍尔态

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摘要

We examine the existence of the interaction-generated quantum anomalous Hall phase on the honeycomb lattice. For the spinless model at half-filling, the existence of a quantum anomalous Hall phase (Chern insulator phase) has been predicted using mean-field methods. However, recent exact diagonalization studies for small clusters with periodic boundary conditions have not found a clear sign of an interaction-driven Chern insulator phase. We use the exact diagonalization method to study properties of small clusters with open boundary conditions, and contrary to previous studies, we find clear signatures of the topological phase transition for finite-size clusters. We also examine the applicability of the entangled-plaquette-state (correlator-product-state) ansatz to describe the ground states of the system. Within this approach the lattice is covered with plaquettes and the ground-state wave function is written in terms of the plaquette coefficients. Configurational weights can then be optimized using a variational Monte Carlo algorithm. Using the entangled-plaquette-state ansatz we study the ground-state properties of the system for larger system sizes and show that the results agree with the exact diagonalization results for small clusters. This confirms the validity of the entangled-plaquette-state ansatz to describe the ground states of the system and provides further confirmation of the existence of the quantum anomalous Hall phase in the thermodynamic limit, as predicted by mean-field theory calculations.
机译：我们检查了蜂窝晶格上相互作用产生的量子异常霍尔相的存在。对于半填充时的无旋转模型，已经使用平均场方法预测了量子异常霍尔相（Chern绝缘子相）的存在。但是，最近对具有周期性边界条件的小簇的精确对角化研究尚未发现相互作用驱动的Chern绝缘子相的明显迹象。我们使用精确的对角线化方法来研究具有开放边界条件的小聚类的性质，并且与先前的研究相反，我们发现了有限大小聚类的拓扑相变的清晰特征。我们还检查了缠结的板状状态（关联产品状态）ansatz的适用性，以描述系统的基态。在这种方法中，晶格覆盖有球拍，并且根据球拍系数写出基态波函数。然后可以使用变分蒙特卡洛算法优化配置权重。我们使用纠缠的板状态ansatz研究了较大系统尺寸的系统的基态特性，并表明该结果与小簇的精确对角化结果一致。这证实了缠结球状状态安萨兹描述系统基态的有效性，并进一步证实了均热场理论计算所预测的热力学极限中量子异常霍尔相的存在。

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