Generalized Pseudopotentials for the Anisotropic Fractional Quantum Hall Effect

Abstract

We generalize the notion of Haldane pseudopotentials to anisotropic fractional quantum Hall (FQH) systems which are physically realized, e.g., in tilted magnetic field experiments or anisotropic band structures. This formalism allows us to expand any translation-invariant interaction over a complete basis, and directly reveals the intrinsic metric of incompressible FQH fluids. We show that purely anisotropic pseudopotentials give rise to new types of bound states for small particle clusters in the infinite plane, and can be used as a diagnostic of FQH nematic order. We also demonstrate that generalized pseudopotentials quantify the anisotropic contribution to the effective interaction potential, which can be particularly large in models of fractional Chern insulators.

4+ pages, 5 figures, published version with supplementary materials, comments welcome

References in corpus (11)

• High temperature fractional quantum Hall states
• Fractional quantum Hall states at zero magnetic field
• Nearly-flat bands with nontrivial topology
• Fractional quantum Hall effect in the absence of Landau levels
• Position-Momentum Duality and Fractional Quantum Hall Effect in Chern Insulators
• Framing Anomaly in the Effective Theory of Fractional Quantum Hall Effect
• Bloch Model Wavefunctions and Pseudopotentials for All Fractional Chern Insulators
• Low-energy effective theory in the bulk for transport in a topological phase
• Band mass anisotropy and the intrinsic metric of fractional quantum Hall systems
• Theory of Nematic Fractional Quantum Hall State
• Fractional quantum Hall states in two-dimensional electron systems with anisotropic interactions

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