Effect of Laughlin correlations on crystalline mean field solutions of the 2DEG in FQHE regime

TL;DR

This study numerically evaluates how Laughlin correlations influence crystalline mean field solutions of the 2DEG in the FQHE regime, showing that mixed wavefunctions can have lower energy than pure Laughlin states.

Contribution

It introduces a new class of trial wavefunctions combining Laughlin liquid and crystalline correlations, with evidence they may be energetically favorable in the thermodynamic limit.

Findings

Mixed wavefunctions have lower energy than Laughlin states in finite samples.

Preliminary results suggest this energy advantage persists as sample size increases.

The results are relevant to recent experiments indicating periodic structures in the 2DEG at fractional fillings.

Abstract

The energy per particle of many body wavefunctions that mix Laughlin liquid with crystalline correlations for periodic samples in the Haldane-Rezayi configuration is numerically evaluated for periodic samples. The Monte Carlo algorithm is employed and the wave functions are constructed in such a way that have the same zeroes as the periodic Laughlin states. Results with up to 16 particles show that these trial wavefunctions have lower energy than the periodic Laughlin states for finite samples even at $\nu=1/3$. Preliminary results for 36 particles suggest that this tendency could reach the thermodynamic limit. These results get relevance in view of the very recent experimental measures that indicate the presence of periodic structures in the 2DEG for extremely small temperatures and clean samples, inclusive at main FQHE filling fractions $\nu=1/3,2/3 $.