Phase Transitions in Quantum Dots

TL;DR

This paper investigates phase transitions in quantum dots, showing a gradual transition to a spin-polarized Wigner crystal with increasing magnetic field, using Hartree-Fock and Monte Carlo methods.

Contribution

It introduces a detailed phase diagram and ground state energies for quantum dots, incorporating a Jastrow ansatz and exploring magic numbers and heat capacity effects.

Findings

Quantum dots undergo a transition to a spin-polarized Wigner crystal.

Ground state energies and phase diagram are determined.

Heat capacity of deformed states is calculated.

Abstract

We perform Hartree-Fock calculations to show that quantum dots (i.e. two dimensional systems of up to twenty interacting electrons in an external parabolic potential) undergo a gradual transition to a spin-polarized Wigner crystal with increasing magnetic field strength. The phase diagram and ground state energies have been determined. We tried to improve the ground state of the Wigner crystal by introducing a Jastrow ansatz for the wavefunction and performing a variational Monte Carlo calculation. The existence of so called magic numbers was also investigated. Finally, we also calculated the heat capacity associated with the rotational degree of freedom of deformed many-body states.