Generalized Pseudopotentials for the Anisotropic Fractional Quantum Hall Effect

TL;DR

This paper extends Haldane pseudopotentials to anisotropic fractional quantum Hall systems, enabling analysis of anisotropic interactions, revealing new bound states, and diagnosing nematic order in FQH and fractional Chern insulators.

Contribution

It introduces a generalized pseudopotential formalism for anisotropic FQH systems, allowing detailed analysis of anisotropic interactions and their effects.

Findings

Anisotropic pseudopotentials lead to new bound states in particle clusters.

The formalism reveals the intrinsic metric of FQH fluids.

Generalized pseudopotentials quantify anisotropic contributions in fractional Chern insulators.

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.