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

TL;DR

This paper demonstrates that two-dimensional fermions with repulsive interactions exhibit universal strongly-correlated behavior near the quantum freezing point, using quantum Monte Carlo analysis and variational methods to predict phase transitions and collective excitations.

Contribution

It introduces a quantum generalization of the Hansen-Verlet criterion for 2D fermions and provides a variational approach that accurately predicts the freezing transition and correlation effects.

Findings

Universal behavior in 2D fermions near freezing point

Variational method captures over 95% of correlation energy

Predicted collective monopole oscillation frequencies

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 95% 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.