Composite-Boson Ansatz for Fractional Quantum Hall Manifolds of Lattice Bosons at Generic Fillings $\nu<1/2$
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 \(\nu<1/2\). 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.