Pseudopotentials for Multi-particle Interactions in the Quantum Hall Regime

TL;DR

This paper extends Haldane's pseudopotential formalism to multi-particle interactions in the fractional quantum Hall regime, providing a new framework for understanding complex many-body effects.

Contribution

It introduces a generalized pseudopotential construction for M-body interactions, broadening the analytical tools available for quantum Hall physics.

Findings

Developed a formalism for M-body pseudopotentials

Provided insights into multi-particle interaction effects

Enhanced understanding of quantum Hall states

Abstract

In fractional quantum Hall physics, the Hilbert space is projected to a single Landau level and the entire Hamiltonian consists of just the projected inter-electron interaction. Haldane's pseudopotential formalism has been an extremely useful tool both for understanding these interactions, and for understanding the quantum Hall states that result. In the current paper we consider the analogue of this pseudopotential construction that results from general M-body interactions rather than the usual (Coulomb) two-body interaction.