Ground state, quasi-hole, a pair of quasihole wavefunctions and instability in bilayer quantum Hall systems

TL;DR

This paper derives and analyzes wavefunctions for bilayer quantum Hall systems using composite boson theory, revealing differences from known states, distance-dependent features, and potential instabilities leading to density wave formation.

Contribution

It provides new wavefunctions for bilayer quantum Hall states, highlighting differences from the (111) state and uncovering instability mechanisms.

Findings

Ground state wavefunction differs from (111) at finite distance d.

Quasi-hole wavefunctions include non-trivial normalization factors.

Instability in the spin part leads to pseudo-spin density wave formation.

Abstract

Bilayer quantum Hall system (BLQH) differ from its single layer counterparts (SLQH) by its symmetry breaking ground state and associated neutral gapless mode in the pseudo-spin sector. Due to the gapless mode, qualitatively good groundstate and low energy excited state wavefunctions at any finite distance is still unknown. We investigate this important open problem by the Composite Boson (CB) theory developed by one of the authors to study BLQH systematically. We derive the ground state, quasi-hole and a pair of quasihole wavefunctions from the CB theory and its dual action. We find that the ground state wavefunction differs from the well known $ (111) $ wavefunction at any finite $ d $. In addition to commonly known multiplicative factors, the quasi-hole and a pair of quasi-holes wavefunctions also contain non-trivial normalization factors multiplying the correct ground state wavefunction. All the distance dependencies in all the wavefunctions are encoded in the spin part of the ground state wavefunction. The instability encoded in the spin part of the groundstate wavefunction leads to the pseudo-spin density wave formation proposed by one of the authors previously. Some subtleties related to the Lowest Landau Level (LLL) projection of the wavefunctions are briefly discussed.