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.
$Phase diagram of the v = 5/2 fractional quantum Hall effect: Effects of Landau-level mixing and nonzero width [pdf]$ Paper $Phase diagram of the v = 5/2 fractional quantum Hall effect: Effects of Landau-level mixing and nonzero width [link]$ Website doi abstract bibtex

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},
 month = {4},
 day = {2},
 id = {6bff99a6-0f5b-37c6-8b35-a36d30a08a65},
 created = {2020-06-19T15:33:17.579Z},
 file_attached = {true},
 profile_id = {004c1ae0-7ed4-35f3-b39b-28665b4ab9a2},
 last_modified = {2021-05-06T16:13:20.245Z},
 read = {true},
 starred = {false},
 authored = {true},
 confirmed = {true},
 hidden = {false},
 citation_key = {Pakrouski2015},
 source_type = {JOUR},
 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}
}

Downloads: 0

{"_id":"uFNGc8BtPoGSqZviS","bibbaseid":"pakrouski-peterson-jolicoeur-scarola-nayak-troyer-phasediagramofthev52fractionalquantumhalleffecteffectsoflandaulevelmixingandnonzerowidth-2015","downloads":0,"creationDate":"2017-11-18T02:29:51.263Z","title":"Phase diagram of the v = 5/2 fractional quantum Hall effect: Effects of Landau-level mixing and nonzero width","author_short":["Pakrouski, K.","Peterson, M., M., R.","Jolicoeur, T.","Scarola, V., W.","Nayak, C.","Troyer, M."],"year":2015,"bibtype":"article","biburl":"https://bibbase.org/service/mendeley/004c1ae0-7ed4-35f3-b39b-28665b4ab9a2","bibdata":{"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","month":"4","day":"2","id":"6bff99a6-0f5b-37c6-8b35-a36d30a08a65","created":"2020-06-19T15:33:17.579Z","file_attached":"true","profile_id":"004c1ae0-7ed4-35f3-b39b-28665b4ab9a2","last_modified":"2021-05-06T16:13:20.245Z","read":"true","starred":false,"authored":"true","confirmed":"true","hidden":false,"citation_key":"Pakrouski2015","source_type":"JOUR","notes":"From Duplicate 1 (Phase diagram of the v = 5/2 fractional quantum hall effect: Effects of Landau-level mixing and nonzero width - Pakrouski, Kiryl; Peterson, Michael R.; Jolicoeur, Thierry; Scarola, Vito W.; Nayak, Chetan; Troyer, Matthias) Owner: scarola 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","bibtex":"@article{\n title = {Phase diagram of the v = 5/2 fractional quantum Hall effect: Effects of Landau-level mixing and nonzero width},\n type = {article},\n year = {2015},\n pages = {021004},\n volume = {5},\n websites = {http://dx.doi.org/10.1103/PhysRevX.5.021004},\n month = {4},\n day = {2},\n id = {6bff99a6-0f5b-37c6-8b35-a36d30a08a65},\n created = {2020-06-19T15:33:17.579Z},\n file_attached = {true},\n profile_id = {004c1ae0-7ed4-35f3-b39b-28665b4ab9a2},\n last_modified = {2021-05-06T16:13:20.245Z},\n read = {true},\n starred = {false},\n authored = {true},\n confirmed = {true},\n hidden = {false},\n citation_key = {Pakrouski2015},\n source_type = {JOUR},\n notes = {From Duplicate 1 (Phase diagram of the v = 5/2 fractional quantum hall effect: Effects of Landau-level mixing and nonzero width - Pakrouski, Kiryl; Peterson, Michael R.; Jolicoeur, Thierry; Scarola, Vito W.; Nayak, Chetan; Troyer, Matthias) Owner: scarola Added to JabRef: 2015.09.08},\n private_publication = {false},\n 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.},\n bibtype = {article},\n author = {Pakrouski, Kiryl and Peterson, M.R. Michael R. and Jolicoeur, Thierry and Scarola, Vito W. and Nayak, Chetan and Troyer, Matthias},\n doi = {10.1103/PhysRevX.5.021004},\n journal = {Physical Review X},\n number = {2}\n}","author_short":["Pakrouski, K.","Peterson, M., M., R.","Jolicoeur, T.","Scarola, V., W.","Nayak, C.","Troyer, M."],"urls":{"Paper":"https://bibbase.org/service/mendeley/004c1ae0-7ed4-35f3-b39b-28665b4ab9a2/file/55e9c4aa-eb36-4f57-6950-0f6b2afeb70c/Pakrouski_et_al_2015_Phase_diagram_of_the_v__52_fractional_quantum_hall_effect_Effects_of_Landau_level_mixing_and_nonzer.pdf.pdf","Website":"http://dx.doi.org/10.1103/PhysRevX.5.021004"},"biburl":"https://bibbase.org/service/mendeley/004c1ae0-7ed4-35f3-b39b-28665b4ab9a2","bibbaseid":"pakrouski-peterson-jolicoeur-scarola-nayak-troyer-phasediagramofthev52fractionalquantumhalleffecteffectsoflandaulevelmixingandnonzerowidth-2015","role":"author","metadata":{"authorlinks":{"scarola, v":"https://bibbase.org/service/mendeley/004c1ae0-7ed4-35f3-b39b-28665b4ab9a2"}},"downloads":0,"html":""},"search_terms":["phase","diagram","fractional","quantum","hall","effect","effects","landau","level","mixing","nonzero","width","pakrouski","peterson","jolicoeur","scarola","nayak","troyer"],"keywords":[],"authorIDs":["39wevj2fTXkkcvngx","4jwBWvfTSfDTMCr5Q","52i2GToGbfvGtn45E","5a0f9766545c47e43000000c","5de7fd909b61e8de01000034","5de93c8cb8c3f8de010000af","5e00a76d05b03cf30100007a","5e04be62d2e808e8010000ca","5e11cb2de49b0bdf010000ba","5e139a150d0b99de0100000d","5e1644b028f1c0de010000bb","5e194f6486b4aade010000ef","5e1be0e84c869ade0100004f","5e2c274beb4d3ddf01000055","5e2cc95a972628f201000040","5e2fc860e075a2df01000090","5e339b1917f2c9de01000072","5e3c730067788ede01000165","5e4691fd71278bde010001a6","5e4c3516c1eb51df010000e5","5e4c4caf271596df01000029","5e57fd40a38020de01000119","5e581f4d6a456fde01000154","5e5af778038583de010000d7","5e5d1d98168391de01000060","5e5eb8742fd1fade010001bd","5e66969144d2c4de01000119","6iuZmTvP5b8GthBMC","9porMkmrNg99w6Q4o","HLxCEadiEfXdnPiiX","JEG4vH3Y4u8TX7GaK","JyuLoJZSKsiHSLN4S","PDav5H8KjoQKgWNPQ","aqXRxKBsXyXKxCQyg","e4xFjPvgrhRwJycyu","h6S7CfpgZJA33699M","hAnj2Q2PRyKAMJxn3","hZAGuxzXnmMh6ogso","honhaTuooy2jijuRA","iEELiMjdr4wZaigAe","ke5gHrJKWPuCDtHBS","wvphCPyd8yH7kMG5s","zqzBMncc4o9w2om2w"],"dataSources":["3hvXS94a6LrrsHXsS","ya2CyA73rpZseyrZ8","q9AemAnoxjKBeqdKn","2252seNhipfTmjEBQ"]}