Abelian and non-Abelian states inν=2/3bilayer fractional quantum Hall systems

Abstract

There are several possible theoretically allowed non-Abelian fractional quantum Hall (FQH) states that could potentially be realized in one-and two-component FQH systems at total filling fraction ν = n + 2/3, for integer n. Some of these states even possess quasiparticles with non-Abelian statistics that are powerful enough for universal topological quantum computation, and are thus of particular interest. Here, we initiate a systematic numerical study, using both exact diagonalization and variational Monte Carlo, to investigate the phase diagram of FQH systems at total filling fraction ν = n + 2/3, including in particular the possibility of the non-Abelian Z4 parafermion state. In ν = 2/3 bilayers, we determine the phase diagram as a function of interlayer tunneling and repulsion, finding only three competing Abelian states, without the Z4 state. On the other hand, in singlecomponent systems at ν = 8/3, we find that the Z4 parafermion state has significantly higher overlap with the exact ground state than the Laughlin state, together with a larger gap, suggesting that the experimentally observed ν = 8/3 state may be non-Abelian. Our results from the two complementary numerical techniques agree well with each other qualitatively.

Landau-Ginzburg theories of non-Abelian quantum Hall states from non-Abelian bosonization

“…Such projections have been implemented at the formal level of the edge CFT ("ideal") wave function [40,41] and in coupled wire constructions [42,43]. Numerical studies of bilayer systems have also lent support to this idea [44][45][46][47][48][49][50]. However, a robust bulk LG description of generic non-Abelian FQH states continues to be lacking.…”

Quantum Entanglement as a Diagnostic of Phase Transitions in Disordered Fractional Quantum Hall Liquids

“…However, unlike the dramatic phase-transition signal in the entanglement entropy derivative, we find a gradual reduction of level repulsion only deep in the Anderson insulating phase. Introduction.-Following the advances in understanding the fascinatingly complex phase diagram of two-dimensional electron systems in a strong perpendicular magnetic field in the fractional quantum Hall (FQH) regime [1][2][3][4][5][6][7][8][9][10][11][12], there has been intense interest in phase transitions in topological systems [13][14][15][16][17]. Disorder is a ubiquitous ingredient that may affect, even drive such phase transitions.…”

Non-Abelian quasiholes in lattice Moore-Read states and parent Hamiltonians

“…The fractional quantum Hall effect was a pioneering breakthrough in the context of topological systems [1][2][3][4] . This phenomenon unveils an exotic phase of matter [5][6][7][8][9][10][11][12][13][14][15][16] and is obtainable at very low temperatures.…”