We study the phase diagram of quantum Hall bilayer systems with total filing ν_{T}=1/2+1/2 of the lowest Landau level as a function of layer distances d. Based on numerical exact diagonalization calculations, we obtain three distinct phases, including an exciton superfluid phase with spontaneous interlayer coherence at small d, a composite Fermi liquid at large d, and an intermediate phase for 1.1<d/l_{B}<1.8 (l_{B} is the magnetic length). The transition from the exciton superfluid to the intermediate phase is identified by (i) a dramatic change in the Berry curvature of the ground state under twisted boundary conditions on the two layers and (ii) an energy level crossing of the first excited state. The transition from the intermediate phase to the composite Fermi liquid is identified by the vanishing of the exciton superfluid stiffness. Furthermore, from our finite-size study, the energy cost of transferring one electron between the layers shows an even-odd effect and possibly extrapolates to a finite value in the thermodynamic limit, indicating the enhanced intralayer correlation. Our identification of an intermediate phase and its distinctive features shed new light on the theoretical understanding of the quantum Hall bilayer system at total filling ν_{T}=1.We study the phase diagram of quantum Hall bilayer systems with total filing ν_{T}=1/2+1/2 of the lowest Landau level as a function of layer distances d. Based on numerical exact diagonalization calculations, we obtain three distinct phases, including an exciton superfluid phase with spontaneous interlayer coherence at small d, a composite Fermi liquid at large d, and an intermediate phase for 1.1<d/l_{B}<1.8 (l_{B} is the magnetic length). The transition from the exciton superfluid to the intermediate phase is identified by (i) a dramatic change in the Berry curvature of the ground state under twisted boundary conditions on the two layers and (ii) an energy level crossing of the first excited state. The transition from the intermediate phase to the composite Fermi liquid is identified by the vanishing of the exciton superfluid stiffness. Furthermore, from our finite-size study, the energy cost of transferring one electron between the layers shows an even-odd effect and possibly extrapolates to a finite value in the thermodynamic limit, indicating the enhanced intralayer correlation. Our identification of an intermediate phase and its distinctive features shed new light on the theoretical understanding of the quantum Hall bilayer system at total filling ν_{T}=1.

arXiv:1703.08463Physical Review LettersOct 23, 201723 citations

Numerical Investigation of the Fractional Quantum Hall Effect

D. Yoshioka

Recent Progress in Many-Body TheoriesJan 1, 19880 citations

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

Michael R. Peterson, Yang-Le Wu, Meng Cheng +3 more

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 $\ensuremath{\nu}=n+2/3$, 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 $\ensuremath{\nu}=n+2/3$, including in particular the possibility of the non-Abelian ${Z}_{4}$ parafermion state. In $\ensuremath{\nu}=2/3$ bilayers we determine the phase diagram as a function of interlayer tunneling and repulsion, finding only three competing Abelian states, without the ${Z}_{4}$ state. On the other hand, in single-component systems at $\ensuremath{\nu}=8/3$, we find that the ${Z}_{4}$ 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 $\ensuremath{\nu}=8/3$ state may be non-Abelian. Our results from the two complementary numerical techniques agree well with each other qualitatively.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 $\ensuremath{\nu}=n+2/3$, 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 $\ensuremath{\nu}=n+2/3$, including in particular the possibility of the non-Abelian ${Z}_{4}$ parafermion state. In $\ensuremath{\nu}=2/3$ bilayers we determine the phase diagram as a function of interlayer tunneling and repulsion, finding only three competing Abelian states, without the ${Z}_{4}$ state. On the other hand, in single-component systems at $\ensuremath{\nu}=8/3$, we find that the ${Z}_{4}$ 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 $\ensuremath{\nu}=8/3$ state may be non-Abelian. Our results from the two complementary numerical techniques agree well with each other qualitatively.

arXiv:1502.02671Physical Review BJul 2, 201545 citations

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 $\ensuremath{\nu}=n+2/3$, including in particular the possibility of the non-Abelian

{Z}_{4}

parafermion state. In $\ensuremath{\nu}=2/3$ bilayers we determine the phase diagram as a function of interlayer tunneling and repulsion, finding only three competing Abelian states, without the

{Z}_{4}

state. On the other hand, in single-component systems at $\ensuremath{\nu}=8/3$, we find that the

{Z}_{4}

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 $\ensuremath{\nu}=8/3$ state may be non-Abelian. Our results from the two complementary numerical techniques agree well with each other qualitatively.