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

TL;DR

This paper derives analytical expressions for three-body interactions in fractional quantum Hall systems, highlighting how realistic band structures and breaking Galilean invariance influence topological phases and can be computed efficiently.

Contribution

It provides a general formalism for calculating three-body pseudopotentials in FQH systems without assuming rotational or Galilean invariance, applicable to realistic materials.

Findings

Finite thickness and screening suppress three-body interactions.

Breaking Galilean invariance can induce phase transitions between Moore-Read states.

Analytical expressions facilitate high-precision numerical studies.

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.