Nonlocal density interactions in auxiliary-field quantum Monte Carlo simulations: application to the square lattice bilayer and honeycomb lattice
Nonlocal density interactions in auxiliary-field quantum Monte Carlo simulations: application to the square lattice bilayer and honeycomb lattice
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DOI：
10.1103/physrevb.92.195154
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发表时间：
2015-09
影响因子：
3.7
通讯作者：
Michael Golor;S. Wessel
中科院分区：
文献类型：
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作者：
Michael Golor;S. Wessel
我们考虑一种基于键中心辅助场量子蒙特卡罗的有效方案来模拟二维非局域密度-密度相互作用的费米子哈伯德模型。结果表明，模拟在有限的、受限制的参数范围内没有符号问题。使用这种方法，我们首先研究半填充方形晶格双层的哈伯德模型，除了局部斥力之外还包括层间斥力项，并在可访问参数区域内呈现基态相图。从没有层间排斥的反铁磁有序态开始，发现层间相互作用会破坏反铁磁有序态的稳定，导致带绝缘体态。此外，对于足够强的层间隧道效应，我们还观察到沿相等耦合线出现混合 D-Mott 和 S-Mott 特征的直接二聚体产物状态。我们在强耦合微扰理论中讨论该状态的稳定范围。此外，我们考虑具有次近邻相互作用的蜂窝晶格上的哈伯德模型。发现这种相互作用可以增强半金属区域内的电荷密度和自旋电流相关性。然而，在可访问的参数区域内，它们不能稳定长程电荷密度波序，也不能稳定量子自旋霍尔态，并且我们观察到的唯一绝缘态表现出长程反铁磁性。
We consider an efficient scheme to simulate fermionic Hubbard models with nonlocal density-density interactions in two dimensions, based on bond-centered auxiliary-field quantum Monte Carlo. The simulations are shown to be sign-problem free within a finite, restricted parameter range. Using this approach, we first study the Hubbard model on the half-filled square lattice bilayer, including an interlayer repulsion term in addition to the local repulsion, and present the ground state phase diagram within the accessible parameter region. Starting from the antiferromagnetically ordered state in the absence of interlayer repulsion, the interlayer interactions are found to destabilize the antiferromagnetic order, leading to a band insulator state. Moreover, for sufficiently strong interlayer tunneling, we also observe the emergence of a direct dimer product state of mixed D-Mott and S-Mott character along the equal coupling line. We discuss the stability range of this state within strong-coupling perturbation theory. Furthermore, we consider the Hubbard model on the honeycomb lattice with next-nearest-neighbor interactions. Such an interaction is found to enhance both charge density and spin-current correlations within the semimetallic region. However, inside the accessible parameter region, they do not stabilize long-ranged charge density wave order nor a quantum spin Hall state, and the only insulating state that we observe exhibits long-range antiferromagnetism.