Laughlin-Jastrow-correlated Wigner crystal in a strong magnetic field

TL;DR

This paper introduces a new trial wavefunction for a two-dimensional Wigner crystal in a strong magnetic field, incorporating Laughlin-Jastrow correlations, and demonstrates its lower energy compared to previous models through quantum Monte Carlo simulations.

Contribution

It proposes a novel correlated wavefunction for Wigner crystals that accounts for composite fermion or boson behavior, improving energy estimates in strong magnetic fields.

Findings

Wavefunctions have lower energy than previous models.

Results align with experimental transition points.

Exchange effects are negligible at small filling factors.

Abstract

We propose a new ground state trial wavefunction for a two-dimensional Wigner crystal in a strong perpendicular magnetic field. The wavefunction includes Laughlin-Jastrow correlations between electron pairs, and may be interpreted as a crystal state of composite fermions or composite bosons. Treating the power $m$ of the Laughlin-Jastrow factor as a variational parameter, we use quantum Monte Carlo simulations to compute the energy of these new states. We find that our wavefunctions have lower energy than existing crystalline wavefunctions in the lowest Landau level. Our results are consistent with experimental observations of the filling factor at which the transition between the fractional quantum Hall liquid and the Wigner crystal occurs for electron systems. Exchange contributions to the wavefunctions are estimated quantitatively and shown to be negligible for sufficiently small filling factors.