AI 中文总结
本文针对通用填充ν<1/2的格点玻色子分数量子霍尔流形，提出复合玻色子拟设，通过计算多体陈数等验证其特征，建立了相关微观框架。
AI 中文摘要
霍夫施塔特系统为分数量子霍尔物理提供了格点实现途径，但其低能流形常缺乏简洁的波函数描述。本文针对低通量霍夫施塔特-玻色-哈伯德模型在圆环上通用填充ν<1/2时的一大类有限尺寸格点分裂劳夫林准空穴流形，提出一种复合玻色子拟设。为每个玻色子附加两个涡旋可得到通量降低的轨道，基于此构建多体试探基，其平移分辨的秩重现了预期的低能流形维度，且为此前通过广义排斥规则和细圆环论证推断出的准空穴计数提供了复合玻色子诠释。对于较小系统，在最低带投影的拟设空间内对角化可紧密重现精确的投影谱；而变分蒙特卡罗则将秩和能量分析扩展到显式子空间构建成本高昂的更大系统。为探测这些流形的分数量子霍尔特征，本文计算了其多体陈数，结果显示局域化的附加通量激发表现出准空穴类行为，具有分数密度耗尽和无阿哈罗诺夫-玻姆效应的编织相位，二者均跟踪有效填充率。综上，这些结果建立了一个微观复合玻色子框架，用于组织一大类半填充以下的格点玻色子分数量子霍尔流形。
英文摘要
Hofstadter systems provide a lattice route to fractional quantum Hall physics, but their low-energy manifolds often lack simple wave-function descriptions. Here we present a composite-boson ansatz for a broad family of finite-size lattice-split Laughlin-quasihole manifolds in the low-flux Hofstadter--Bose--Hubbard model on a torus at generic fillings \(ν<1/2\). Attaching two vortices to each boson yields reduced-flux orbitals from which we construct a many-body trial basis. Its translation-resolved rank reproduces the expected low-energy-manifold dimension and provides a composite-boson interpretation of the established quasihole counting previously inferred from generalized exclusion rules and thin-torus arguments. For smaller systems, diagonalization within the lowest-band-projected ansatz span closely reproduces the exact projected spectrum, while variational Monte Carlo extends the rank and energetic analysis to larger systems for which explicit subspace construction becomes costly. To probe the fractional quantum Hall character of these manifolds, we calculate their many-body Chern-numbers and show that localized added-flux excitations exhibit quasihole-like behavior, with fractional density depletion and an Aharonov--Bohm-free braiding phase that both track the effective filling. Together, these results establish a microscopic composite-boson framework for organizing a broad family of sub-half-filled fractional quantum Hall manifolds of lattice bosons.
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