1:30 pm MCP 201
Generalized Higher Landau Levels: Quantized Integrated Trace Formula and Implication for non-Abelian States.
Quantum geometry is a fundamental concept to characterize the local properties of quantum states varying in a parameter space. Recent works demonstrated that saturating certain quantum geometric bounds allows a topological Chern band to share many essential features with the lowest Landau level, facilitating fractionalized phases in moire flat bands. In this work, we systematically extend the consequence and universality of saturated geometric bounds to arbitrary Landau levels by introducing a set of single-electron states, which we term as ``generalized Landau levels''. These generalized Landau levels exhibit exactly quantized values of integrated trace of quantum metric determined by their corresponding Landau level indices, regardless of the nonuniformity of their quantum geometric quantities. We analytically derive all geometric quantities for individual generalized Landau levels and their super-positions, discuss their interrelationship, and compare them with the theory of holomorphic curves. We further propose a model of generalized Landau levels to capture a large portion of the single-particle Hilbert space of a generic Chern band analogous to the first Landau level. Using this model, we employ large-scale exact diagonalization to identify a single-particle geometric criterion for permitting the non-Abelian Moore-Read phase at half-filling. We expect that generalized Landau levels will serve as a systematic tool for analyzing topological Chern bands and fractionalized phases therein.