In a lattice model subject to a perpendicular magnetic field, when the lattice constant is comparable to the magnetic length, one enters the “Hofstadter regime,” where continuum Landau levels become fractal magnetic Bloch bands. Strong mixing between bands alters the nature of the resulting quantum phases compared to the continuum limit; lattice potential, magnetic field, and Coulomb interaction must be treated on equal footing. Using determinant quantum Monte Carlo and density matrix renormalization group techniques, we study this regime numerically in the context of the Hubbard-Hofstadter model on a triangular lattice. In the field-filling phase diagram, we find a broad wedge-shaped region of ferromagnetic ground states for filling factor 𝜈≤1, bounded below by filling factor 𝜈=1 and bounded above by half filling the lowest Hofstadter subband. We observe signatures of SU(2) quantum Hall ferromagnetism at filling factors 𝜈=1 and 𝜈=3. The phases near 𝜈=1 are particle-hole asymmetric, and we observe a rapid decrease in ground-state spin polarization consistent with the formation of skyrmions only on the electron doped side. At large fields, above the ferromagnetic wedge, we observe a low-spin metallic region with spin correlations peaked at small momenta. We argue that the phenomenology of this region likely results from exchange interaction mixing fractal Hofstadter subbands. The phase diagram derived beyond the continuum limit points to a rich landscape to explore interaction effects in magnetic Bloch bands.

中文翻译：

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三角 Hubbard-Hofstadter 模型中的粒子空穴不对称铁磁性和自旋织构


在受垂直磁场影响的晶格模型中，当晶格常数与磁长度相当时，就会进入“霍夫施塔特状态”，其中连续体朗道能级变成分形磁布洛赫带。与连续谱极限相比，谱带之间的强烈混合会改变所得量子相位的性质;晶格电位、磁场和库仑相互作用必须同等对待。使用行列式量子蒙特卡洛和密度矩阵重整化群技术，我们在三角晶格上的 Hubbard-Hofstadter 模型的背景下对这种状态进行了数值研究。在场填充相图中，我们发现填充因子 ν≤1 的铁磁基态的宽楔形区域，下方以填充因子 ν=1 为界，上方以填充最低 Hofstadter 子带的一半为界。我们在填充因子 ν=1 和 ν=3 处观察到 SU（2） 量子霍尔铁磁性的特征。ν=1 附近的相位是粒子-空穴不对称的，我们观察到基态自旋极化的快速降低，这与仅在电子掺杂侧形成斯格明子一致。在铁磁楔形上方的大磁场中，我们观察到一个低自旋金属区域，自旋相关性在小动量处达到峰值。我们认为，该区域的现象学可能是由混合分形 Hofstadter 子带的交换相互作用产生的。超出连续谱极限的相图指向丰富的景观，以探索磁性 Bloch 带中的相互作用效应。