Emergent commensurability from Hilbert space truncation in fractional quantum Hall fluids

We show that model states of fractional quantum Hall fluids at all experimentally detected plateaus can be uniquely determined by imposing translational invariance with a particular scheme of Hilbert space truncation. The truncation is based on classical local exclusion conditions, motivated by constraints on physical measurements. The scheme allows us to identify filling factors, topological shifts, and clustering of topological quantum fluids universally without resorting to microscopic Hamiltonians. This prompts us to propose the notion of emergent commensurability as a fundamental property for many known fractional quantum Hall (FQH) states, which allows us to predict families of new FQH states that can be realized in principle. We also discuss the implications of certain missing states proposed from other phenomenological approaches, and suggest that the physics of the FQH effect could fundamentally arise from the algebraic structure of the Hilbert space in a single Landau level.