Universal behavior of repulsive two-dimensional fermions in the vicinity of the quantum freezing point

¹ Physics Department, Harvard University - Cambridge, MA 02138, USA
² School of Physics and Astronomy, University of Minnesota - Minneapolis, MN 55455, USA
³ Department of Physics, University of California San Diego - La Jolla, CA 92093, USA

Received: 25 March 2013
Accepted: 29 June 2013

Abstract

We show by a meta-analysis of the available Quantum Monte Carlo (QMC) results that two-dimensional fermions with repulsive interactions exhibit universal behavior in the strongly correlated regime, and that their freezing transition can be described using a quantum generalization of the classical Hansen-Verlet freezing criterion. We calculate the liquid-state energy and the freezing point of the 2D dipolar Fermi gas (2DDFG) using a variational method by taking ground-state wave functions of 2D electron gas (2DEG) as trial states. A comparison with the recent fixed-node diffusion Monte Carlo analysis of the 2DDFG shows that our simple variational technique captures more than of the correlation energy, and predicts the freezing transition within the uncertainty bounds of QMC. Finally, we utilize the ground-state wave functions of 2DDFG as trial states and provide a variational account of the effects of finite 2D confinement width. Our results indicate significant beyond mean-field effects. We calculate the frequency of collective monopole oscillations of the quasi-2D dipolar gas as an experimental demonstration of correlation effects.