New Trial Wave Functions for Quantum Hall States at Half Filling

TL;DR

This paper introduces new trial wave functions for half-filling quantum Hall states, constructed via pairing quasielectrons and forming a Laughlin state, with high overlaps to exact states, relevant to unexplored fractional quantum Hall effects.

Contribution

The paper proposes novel trial wave functions for half-filling quantum Hall states based on pairing quasielectrons and forming a Laughlin state, with detailed flux relations and overlap analyses.

Findings

High overlap with exact ground states in the lowest Landau level

Moderate overlap in the second Landau level

Wave functions exhibit Abelian fractional statistics

Abstract

New trial wave functions corresponding to half filling quantum Hall states are proposed. These wave functions are constructed by first pairing up the quasielectrons of the 1/3 Laughlin quantum Hall state, with the same relative angular momentum for each pair, and then making the paired quasielectrons condense into a 1/4 Laughlin state. The quasiparticle excitations of the proposed wave functions carry $\pm1/4$ of electron charge, and obey Abelian fractional statistics. In the spherical geometry, the total flux quanta $N_{\phi}$ is shown to be related to the number of electrons $N$ by $N_{\phi} = 2N-(5-q)$ with $q$ being the relative angular momentum between the quasielectrons in each pair which takes values of non-negative even integers. The overlaps are calculated between the proposed trial wave functions, including the ground state, quasiexciton states, and quasihole states, and the exact states of the finite size systems at $N_{\phi} = 2N-3$. The near unity overlaps are obtained in the lowest Landau level, while the moderate overlaps are obtained in the second Landau level. The relevance of the wave functions to the yet to be discovered fractional quantum Hall effect in the lowest Landau level, as well as the 5/2 quantum Hall effect is also discussed.