Variational quantum Monte Carlo study of two-dimensional Wigner crystals: exchange, correlation, and magnetic field effects

TL;DR

This study uses variational quantum Monte Carlo methods to explore two-dimensional Wigner crystals, analyzing how exchange, correlation, and magnetic fields influence their physical properties and phase transitions.

Contribution

It introduces a variational wavefunction approach that captures the effects of magnetic fields and correlations on 2D Wigner crystals, providing new insights into their ground states and phase behavior.

Findings

Spin-orderings vary across different 2D lattices.

Magnetic fields alter energy scales and electron correlations.

Transition from fractional quantum Hall liquid to Wigner crystal occurs near specific filling factors.

Abstract

The two-dimensional Wigner crystals are studied with the variational quantum Monte Carlo method. The close relationship between the ground-state wavefunction and the collective excitations in the system is illustrated, and used to guide the construction of the ground-state wavefunction of the strongly correlated solid. Exchange, correlation, and magnetic field effects all give rise to distinct physical phenomena. In the absence of any external magnetic field, interesting spin-orderings are observed in the ground-state of the electron crystal in various two-dimensional lattices. In particular, two-dimensional bipartite lattices are shown not to lead necessarily to an antiferromagnetic ground-state. In the quantum Hall effect regime, a strong magnetic field introduces new energy and length scales. The magnetic field quenches the kinetic energy and poses constraints on how the electrons may correlate with each other. Care is taken to ensure the appropriate translational properties of the wavefunction when the system is in a uniform magnetic field. We have examined the exchange, intra-Landau-level correlation as well as Landau-level-mixing effects with various variational wavefunctions. We also determine their dependences on the experimental parameters such as the carrier effective mass at a modulation-doped semiconductor heterojunction. Our results, when combined with some recent calculations for the energy of the fractional quantum Hall liquid including Landau-level-mixing, show quantitatively that in going from $n$-doping to $p$-doping in $GaAS/AlGaAS$ heterojunction systems, the crossover filling factor from the fractional quantum Hall liquid to the Wigner crystal changes from filling factor $\nu \sim 1/5$ to $\nu \sim 1/3$. This lends strong support to the claim that the