Wavefunction approach to the fractional anomalous Hall crystal

Tixuan Tan, Julian May-Mann, Trithep Devakul
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Abstract

We propose fractional anomalous Hall crystals (FAHCs) as possible ground states of strongly interacting electrons in parent bands with Berry curvature. FAHCs are exotic states of matter that spontaneously break continuous translation symmetry to form a fractional Chern insulator. We construct a unified family of variational wavefunctions that describe FAHCs and their competing states in the presence of uniform parent Berry curvature. We calculate their variational energy with Coulomb interactions semi-analytically in the thermodynamic limit. Our analysis reveals that FAHCs can be energetically favorable over both Wigner crystals and integer anomalous Hall crystals for sufficiently strong interactions or flat dispersion.
分数反常霍尔晶体的波函数方法
我们提出分数反常霍尔晶体(FAHCs)是具有贝里曲率的母带中强相互作用电子的可能基态。FAHCs 是自发打破连续平移对称性以形成分数切尔绝缘体的奇异物质状态。我们构建了一个统一的变分波函数族,描述了在均匀母贝里曲率存在下的 FAHC 及其竞争态。我们在热力学极限下半分析地计算了它们与库仑相互作用的变分能量。我们的分析表明,在足够强的相互作用或平坦色散条件下,FAHC 在能量上比 Wigner 晶体和整数反常霍尔晶体都有利。
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