Aspects of Three-body Interactions in Generic Fractional Quantum Hall Systems and Impact of Galilean Invariance Breaking

Abstract

We derive full analytic expressions of three-body interactions from Landau level (LL) mixing in fractional quantum Hall (FQH) systems with Schrieffer-Wolff transformation. The formalism can be applied to any LL, and to very general systems without rotational or Galilean invariance. We illustrate how three-body pseudopotentials (PPs) can be readily computed from the analytical expressions for a wide variety of different systems, and show that for realistic systems, softening the bare Coulomb interactions (e.g. finite thickness or screening) can significantly suppress three-body interactions. More interestingly, for experimental systems without Galilean invariance (which is common for real materials), there is strong evidence that higher orders in band dispersion can drive the Moore-Read state from anti-Pfaffian to Pfaffian phase. Our analysis points to the importance of the realistic band structure details to the non-Abelian topological phases, and the analytical expressions we derived can also be very useful for high fidelity numerical computations.

4+ pages, 3 figures, minor typos corrected, supplementary materials added, comments very welcome

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• The sixteenfold way and the quantum Hall effect at half-integer filling factors
• Topological Interface between Pfaffian and anti-Pfaffian Order in $\nu =5/2$ Quantum Hall Effect
• Microscopic theory for nematic fractional quantum Hall effect
• Geometric Fluctuation of Conformal Hilbert Spaces and Multiple Graviton Modes in Fractional Quantum Hall Effect
• Analytic exposition of the graviton modes in fractional quantum Hall effects and its physical implications
• The Gaffnian and Haffnian: physical relevance of non-unitary CFT for incompressible fractional quantum Hall effect
• Fractional quantum Hall effect from frustration-free Hamiltonians
• Tunable three-body loss in a nonlinear Rydberg medium
• From frustration-free parent Hamiltonians to off-diagonal long-range order: Moore-Read and related states in second quantization
• Edge Induced Topological Phase Transition of the Quantum Hall state at Half Filling
• Flat bands on spherical surface: from Landau levels to giant-quantum-number orbitals
• Exploring Quantum Hall Physics at Ultra-Low Temperatures and at High Pressures