Monte Carlo study of Bose Laughlin wave function for filling factors 1/2, 1/4 and 1/6

TL;DR

This study uses Monte Carlo simulations to compare Bose Laughlin wave function energies with composite fermion Fermi liquid energies at various filling factors, revealing unexpected similarities at certain fractions.

Contribution

It investigates whether Bose Laughlin wave functions can serve as lower energy bounds for CF Fermi liquids at specific filling factors, providing new insights into their energetic relationships.

Findings

At filling factors 1/4 and 1/6, Bose Laughlin energies closely match CF Fermi liquid energies.

At filling factor 1/2, Bose Laughlin energy is significantly lower than CF Fermi liquid energy.

Results challenge assumptions about the descriptive power of Bose Laughlin wave functions for these states.

Abstract

Strongly correlated two-dimensional electronic systems subject to a perpendicular magnetic field at lowest Landau level (LLL) filling factors: 1/2, 1/4 and 1/6 are believed to be composite fermion (CF) Fermi liquid phases. Even though a Bose Laughlin wave function cannot describe these filling factors we investigate whether such a wave function provides a lower energy bound to the true CF Fermi liquid energies. By using Monte Carlo simulations in disk geometry we compute the Bose Laughlin energies and compare them to corresponding results for the spin-polarized LLL CF Fermi liquid state and avalable data from literature.We find the unexpected result that, for filling factors 1/4 and 1/6, the Bose Laughlin ground state energy is practically identical to the true CF liquid energy while this is not the case at 1/2 where the Bose Laughlin ground state energy is sizeably lower than the energy of the CF Fermi liquid state.