Skyrme crystal or Skyrme liquid?

TL;DR

This paper investigates the quantum melting transition of the Skyrme crystal by deriving pair distribution functions for electron liquids and comparing their energies to the solid phase, suggesting the transition occurs near filling factor 1.

Contribution

It provides analytic expressions for pair distribution functions of quantum liquids in the lowest Landau level, enabling energy comparisons with the Skyrme crystal.

Findings

Quantum melting transition may occur closer to ν=1 than previously thought.

Derived pair distribution functions for spin-polarized and unpolarized liquids.

Energy comparisons indicate the liquid phase becomes favorable near ν=1.

Abstract

We address the quantum melting phase transition of the Skyrme crystal. Based on generic sum rules for two-dimensional, isotropic electron quantum liquids in the lowest Landau level, we propose analytic expressions for the pair distribution functions of spin-polarized and spin-unpolarized liquid phases at filling factors $2/3\leq\nu\leq 1$. From the pair distribution functions we calculate the energy of such liquid phases and compare with the energy of the solid phase. The comparison suggests that the quantum melting phase transition may lie much closer to $\nu=1$ than ever expected.