Quantum Hall Fluids on the Haldane Sphere: A Diffusion Monte Carlo Study

TL;DR

This paper introduces a new diffusion Monte Carlo method for simulating quantum Hall fluids on curved surfaces, specifically the Haldane sphere, and investigates the effects of Landau level mixing on energy gaps and quasiparticle stability.

Contribution

A generalized diffusion Monte Carlo approach for curved manifolds is developed and applied to fractional quantum Hall effect studies on the Haldane sphere.

Findings

Landau level mixing reduces the energy gap at ν=1/3

Spin-polarized and spin-reversed quasiparticles have different stabilities

Method provides accurate insights into quantum Hall states on curved geometries

Abstract

A generalized diffusion Monte Carlo method for solving the many-body Schr\"odinger equation on curved manifolds is introduced and used to perform a `fixed-phase' simulation of the fractional quantum Hall effect on the Haldane sphere. This new method is used to study the effect of Landau level mixing on the $\nu=1/3$ energy gap and the relative stability of spin-polarized and spin-reversed quasielectron excitations.