Coulomb and Hard Core Skyrmion Tails

TL;DR

This paper investigates the asymptotic profiles of quantum Hall skyrmions under Coulomb and hard core interactions, demonstrating that the differences in their tails persist after quantization, which is crucial for understanding their statistics.

Contribution

It provides numerical evidence that the distinct asymptotic behaviors of skyrmion tails for Coulomb and hard core interactions remain after quantization at filling factor nu=1.

Findings

Coulomb and hard core skyrmion tails differ significantly in asymptotic behavior.

The difference in tails persists after quantization at nu=1.

Numerical calculations confirm the importance of tail profiles for skyrmion statistics.

Abstract

Quantum Hall skyrmions are quantized solitons of a ferromagnetic O(3) sigma-model. The reference, classical, solutions depend upon the interaction between the electrons and exhibit completely different asymptotic profiles for the physical Coulomb interaction than for the model hard core interaction frequently used to generate variational wavefunctions. In this note we show, by means of numerical calculations on (large) finite size systems at nu=1, that this physically important difference, crucial for a sharp definition of their statistics, persists for the quantized skyrmions at n=1.