Phase diagram of the v = 5/2 fractional quantum Hall effect: Effects of Landau-level mixing and nonzero width

Phase diagram of the v = 5/2 fractional quantum Hall effect: Effects of Landau-level mixing and nonzero width. Pakrouski, K., Peterson, M., M., R., Jolicoeur, T., Scarola, V., W., Nayak, C., & Troyer, M. Physical Review X, 5(2):021004, 4, 2015.
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Interesting non-Abelian states, e.g., the Moore-Read Pfaffian and the anti-Pfaffian, offer candidate descriptions of the v = 5/2 fractional quantum Hall state. But, the significant controversy surrounding the nature of the v = 5/2 state has been hampered by the fact that the competition between these and other states is affected by small parameter changes. To study the phase diagram of the v = 5/2 state, we numerically diagonalize a comprehensive effective Hamiltonian describing the fractional quantum Hall effect of electrons under realistic conditions in GaAs semiconductors. The effective Hamiltonian takes Landau-level mixing into account to lowest order perturbatively in ?, the ratio of the Coulomb energy scale to the cyclotron gap. We also incorporate the nonzero width w of the quantum-well and subband mixing. We find the ground state in both the torus and spherical geometries as a function of ? and w. To sort out the nontrivial competition between candidate ground states, we analyze the following four criteria: its overlap with trial wave functions, the magnitude of energy gaps, the sign of the expectation value of an order parameter for particle-hole symmetry breaking, and the entanglement spectrum. We conclude that the ground state is in the universality class of the Moore-Read Pfaffian state, rather than the anti-Pfaffian, for ? < ?c(w), where ?c(w) is a w-dependent critical value 0.6 ? ?c(w) ? 1. We observe that both Landau-level mixing and nonzero width suppress the excitation gap, but Landau-level mixing has a larger effect in this regard. Our findings have important implications for the identification of non-Abelian fractional quantum Hall states.

@article{
 title = {Phase diagram of the v = 5/2 fractional quantum Hall effect: Effects of Landau-level mixing and nonzero width},
 type = {article},
 year = {2015},
 pages = {021004},
 volume = {5},
 websites = {http://dx.doi.org/10.1103/PhysRevX.5.021004},
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 read = {true},
 starred = {false},
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 notes = {<b>From Duplicate 1 (<i>Phase diagram of the v = 5/2 fractional quantum hall effect: Effects of Landau-level mixing and nonzero width</i> - Pakrouski, Kiryl; Peterson, Michael R.; Jolicoeur, Thierry; Scarola, Vito W.; Nayak, Chetan; Troyer, Matthias)<br/></b><br/>Owner: scarola<br/>Added to JabRef: 2015.09.08},
 private_publication = {false},
 abstract = {Interesting non-Abelian states, e.g., the Moore-Read Pfaffian and the anti-Pfaffian, offer candidate descriptions of the v = 5/2 fractional quantum Hall state. But, the significant controversy surrounding the nature of the v = 5/2 state has been hampered by the fact that the competition between these and other states is affected by small parameter changes. To study the phase diagram of the v = 5/2 state, we numerically diagonalize a comprehensive effective Hamiltonian describing the fractional quantum Hall effect of electrons under realistic conditions in GaAs semiconductors. The effective Hamiltonian takes Landau-level mixing into account to lowest order perturbatively in ?, the ratio of the Coulomb energy scale to the cyclotron gap. We also incorporate the nonzero width w of the quantum-well and subband mixing. We find the ground state in both the torus and spherical geometries as a function of ? and w. To sort out the nontrivial competition between candidate ground states, we analyze the following four criteria: its overlap with trial wave functions, the magnitude of energy gaps, the sign of the expectation value of an order parameter for particle-hole symmetry breaking, and the entanglement spectrum. We conclude that the ground state is in the universality class of the Moore-Read Pfaffian state, rather than the anti-Pfaffian, for ? < ?c(w), where ?c(w) is a w-dependent critical value 0.6 ? ?c(w) ? 1. We observe that both Landau-level mixing and nonzero width suppress the excitation gap, but Landau-level mixing has a larger effect in this regard. Our findings have important implications for the identification of non-Abelian fractional quantum Hall states.},
 bibtype = {article},
 author = {Pakrouski, Kiryl and Peterson, M.R. Michael R. and Jolicoeur, Thierry and Scarola, Vito W. and Nayak, Chetan and Troyer, Matthias},
 doi = {10.1103/PhysRevX.5.021004},
 journal = {Physical Review X},
 number = {2}
}

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