# Quantum melting a Wigner crystal into Hall liquids

## TL;DR

This paper demonstrates through variational Monte Carlo that a magnetic field can melt a Wigner crystal into an integer quantum Hall liquid, driven by quantum oscillations at specific densities.

## Contribution

It provides a theoretical explanation for how magnetic fields induce melting of Wigner crystals into quantum Hall liquids, highlighting the role of quantum oscillations.

## Key findings

- Magnetic field can induce melting of Wigner crystals into quantum Hall liquids.
- Quantum oscillations cause energy cusps at integer filling factors.
- The study identifies density ranges for the quantum melting transition.

## Abstract

Recent experiments have shown that, counterintuitively, applying a magnetic field to a Wigner crystal can induce quantum Hall effects. In this Letter, we use variational Monte Carlo to show that a magnetic field can melt zero-field Wigner crystals into integer quantum Hall liquids. This melting originates from quantum oscillations in the liquid's ground state energy, which develops downward cusps at integer filling factors due to incompressibility. Our calculations establish a range of densities in which this quantum melting transition occurs.