Variational Monte Carlo study of spin polarization stability of fractional quantum Hall states against realistic effects in half-filled Landau levels

TL;DR

This study uses variational Monte Carlo to compare the stability of spin-polarized and unpolarized fractional quantum Hall states under realistic effects, finding the Moore-Read Pfaffian state more favorable in the second Landau level.

Contribution

It provides a detailed energy comparison of the Halperin 331 and Moore-Read Pfaffian states considering realistic deviations, highlighting the robustness of the Pfaffian state in the second Landau level.

Findings

Moore-Read Pfaffian is energetically favored in the second Landau level.

In the lowest Landau level, either state can be lower depending on deviations.

Moderate deviations do not change the stability trend in the second Landau level.

Abstract

We compare ground state energies by variational Monte Carlo of the spin unpolarized Halperin 331 and the spin polarized Moore-Read (MR) Pfaffian fractional quantum Hall states at half-filling of the lowest Landau level (LLL) and the second Landau level (SLL) as a function of small deviations around the Coulomb point via the finite thickness effect and direct alterations to the the first two Haldane pseudopotentials. In the comparison we find that in the LLL, either the 331 state or the MR Pfaffian may be lower in energy depending on the deviations. In the SLL, however, the MR Pfaffian is consistently lower in energy except for large deviations. These results suggest that even under moderate deviations in the interaction potential (through various physical processes such as finite thickness, Landau level mixing, etc.), the MR Pfaffian description is more energetically favorable than the Halperin 331 state in the half-filled SLL (i.e. $\nu = 5/2$), consistent with recent experimental investigations.