Fractional Quantum Hall States at ν = 13 / 5 and 12 / 5 and Their Non-Abelian Nature

Zhu, W.; Gong, S. S.; Haldane, F. D. M.; Sheng, D. N.

doi:10.1103/PhysRevLett.115.126805

Title: Fractional Quantum Hall States at $ν = 13 / 5$ and $12 / 5$ and Their Non-Abelian Nature

Journal Article · Fri Sep 18 00:00:00 EDT 2015 · Physical Review Letters

DOI:https://doi.org/10.1103/PhysRevLett.115.126805· OSTI ID:1221702

Zhu, W.; Gong, S. S.; Haldane, F. D. M.; Sheng, D. N.

View Accepted Manuscript (Publisher)

Cite

Export

Save

Sponsoring Organization:: USDOE Office of Science (SC), Basic Energy Sciences (BES)

Grant/Contract Number:: FG02-06ER46305; SC0002140

OSTI ID:: 1221702

Journal Information:: Physical Review Letters, Journal Name: Physical Review Letters Vol. 115 Journal Issue: 12; ISSN 0031-9007

Publisher:: American Physical SocietyCopyright Statement

Country of Publication:: United States

Language:: English

Citation Metrics:

Cited by: 32 works

Citation information provided by
Web of Science

References (68)

Fractional quantum Hall hierarchy and the second Landau level Bonderson, Parsa; Slingerland, J. K. Physical Review B, Vol. 78, Issue 12 https://doi.org/10.1103/PhysRevB.78.125323	journal	September 2008
Momentum polarization: An entanglement measure of topological spin and chiral central charge Tu, Hong-Hao; Zhang, Yi; Qi, Xiao-Liang Physical Review B, Vol. 88, Issue 19 https://doi.org/10.1103/PhysRevB.88.195412	journal	November 2013
Fractional quantum Hall states at $\frac{1}{3}$ and $\frac{5}{2}$ filling: Density-matrix renormalization group calculations Zhao, Jize; Sheng, D. N.; Haldane, F. D. M. Physical Review B, Vol. 83, Issue 19 https://doi.org/10.1103/PhysRevB.83.195135	journal	May 2011
Some properties of monopole harmonics Wu, Tai Tsun; Yang, Chen Ning Physical Review D, Vol. 16, Issue 4 https://doi.org/10.1103/PhysRevD.16.1018	journal	August 1977
Activation gaps of fractional quantum Hall effect in the second Landau level Choi, H. C.; Kang, W.; Das Sarma, S. Physical Review B, Vol. 77, Issue 8 https://doi.org/10.1103/PhysRevB.77.081301	journal	February 2008
Statistics of Quasiparticles and the Hierarchy of Fractional Quantized Hall States Halperin, B. I. Physical Review Letters, Vol. 52, Issue 18 https://doi.org/10.1103/PhysRevLett.52.1583	journal	April 1984
Paired Hall state at half filling Greiter, Martin; Wen, Xiao-Gang; Wilczek, Frank Physical Review Letters, Vol. 66, Issue 24 https://doi.org/10.1103/PhysRevLett.66.3205	journal	June 1991
Fractional Quantization of the Hall Effect: A Hierarchy of Incompressible Quantum Fluid States Haldane, F. D. M. Physical Review Letters, Vol. 51, Issue 7 https://doi.org/10.1103/PhysRevLett.51.605	journal	August 1983
Beyond paired quantum Hall states: Parafermions and incompressible states in the first excited Landau level Read, N.; Rezayi, E. Physical Review B, Vol. 59, Issue 12 https://doi.org/10.1103/PhysRevB.59.8084	journal	March 1999
Density-matrix renormalization-group method in momentum space Xiang, T. Physical Review B, Vol. 53, Issue 16 https://doi.org/10.1103/PhysRevB.53.R10445	journal	April 1996
Transition from Abelian to non-Abelian quantum liquids in the second Landau level Wójs, Arkadiusz Physical Review B, Vol. 80, Issue 4 https://doi.org/10.1103/PhysRevB.80.041104	journal	July 2009
Electron Correlation in the Second Landau Level: A Competition Between Many Nearly Degenerate Quantum Phases Xia, J. S.; Pan, W.; Vicente, C. L. Physical Review Letters, Vol. 93, Issue 17 https://doi.org/10.1103/PhysRevLett.93.176809	journal	October 2004
Identifying topological order by entanglement entropy Jiang, Hong-Chen; Wang, Zhenghan; Balents, Leon Nature Physics, Vol. 8, Issue 12 https://doi.org/10.1038/nphys2465	journal	November 2012
Entanglement Spectrum as a Generalization of Entanglement Entropy: Identification of Topological Order in Non-Abelian Fractional Quantum Hall Effect States Li, Hui; Haldane, F. D. M. Physical Review Letters, Vol. 101, Issue 1 https://doi.org/10.1103/PhysRevLett.101.010504	journal	July 2008
Topological Characterization of Fractional Quantum Hall Ground States from Microscopic Hamiltonians Zaletel, Michael P.; Mong, Roger S. K.; Pollmann, Frank Physical Review Letters, Vol. 110, Issue 23 https://doi.org/10.1103/PhysRevLett.110.236801	journal	June 2013
Excitation Energies of the Fractional Quantum Hall Effect Yoshioka, Daijiro Journal of the Physical Society of Japan, Vol. 55, Issue 3 https://doi.org/10.1143/JPSJ.55.885	journal	March 1986
Quasi-Particle Properties from Tunneling in the Formula Fractional Quantum Hall State Radu, I. P.; Miller, J. B.; Marcus, C. M. Science, Vol. 320, Issue 5878 https://doi.org/10.1126/science.1157560	journal	May 2008
Detecting Topological Order in a Ground State Wave Function Levin, Michael; Wen, Xiao-Gang Physical Review Letters, Vol. 96, Issue 11 https://doi.org/10.1103/PhysRevLett.96.110405	journal	March 2006
Identifying Non-Abelian Topological Order through Minimal Entangled States Zhu, W.; Gong, S. S.; Haldane, F. D. M. Physical Review Letters, Vol. 112, Issue 9 https://doi.org/10.1103/PhysRevLett.112.096803	journal	March 2014
Half-Filled Lowest Landau Level on a Thin Torus Bergholtz, Emil J.; Karlhede, Anders Physical Review Letters, Vol. 94, Issue 2 https://doi.org/10.1103/PhysRevLett.94.026802	journal	January 2005
Topological Entanglement Entropy Kitaev, Alexei; Preskill, John Physical Review Letters, Vol. 96, Issue 11 https://doi.org/10.1103/PhysRevLett.96.110404	journal	March 2006
Density matrix formulation for quantum renormalization groups White, Steven R. Physical Review Letters, Vol. 69, Issue 19 https://doi.org/10.1103/PhysRevLett.69.2863	journal	November 1992
Bipartite Composite Fermion States Sreejith, G. J.; Tőke, C.; Wójs, A. Physical Review Letters, Vol. 107, Issue 8 https://doi.org/10.1103/PhysRevLett.107.086806	journal	August 2011
Microscopic wave functions for the fractional quantized Hall states at $ν = \frac{2}{5} and \frac{2}{7}$ Morf, R.; d'Ambrumenil, N.; Halperin, B. I. Physical Review B, Vol. 34, Issue 4 https://doi.org/10.1103/PhysRevB.34.3037	journal	August 1986
Entanglement Entropy in Fermionic Laughlin States Haque, Masudul; Zozulya, Oleksandr; Schoutens, Kareljan Physical Review Letters, Vol. 98, Issue 6 https://doi.org/10.1103/PhysRevLett.98.060401	journal	February 2007
Ground-State Phase Diagram of 2D Electrons in a High Landau Level: A Density-Matrix Renormalization Group Study Shibata, Naokazu; Yoshioka, Daijiro Physical Review Letters, Vol. 86, Issue 25 https://doi.org/10.1103/PhysRevLett.86.5755	journal	June 2001
Quasiparticle statistics and braiding from ground-state entanglement Zhang, Yi; Grover, Tarun; Turner, Ari Physical Review B, Vol. 85, Issue 23 https://doi.org/10.1103/PhysRevB.85.235151	journal	June 2012
Topological orders and edge excitations in fractional quantum Hall states Wen, Xiao-Gang Advances in Physics, Vol. 44, Issue 5 https://doi.org/10.1080/00018739500101566	journal	October 1995
Configuration-interaction calculations on the fractional quantum Hall effect Fano, G.; Ortolani, F.; Colombo, E. Physical Review B, Vol. 34, Issue 4 https://doi.org/10.1103/PhysRevB.34.2670	journal	August 1986
Topologically Protected Qubits from a Possible Non-Abelian Fractional Quantum Hall State Das Sarma, Sankar; Freedman, Michael; Nayak, Chetan Physical Review Letters, Vol. 94, Issue 16 https://doi.org/10.1103/PhysRevLett.94.166802	journal	April 2005
Density Matrix Renormalization Group Study of Incompressible Fractional Quantum Hall States Feiguin, A. E.; Rezayi, E.; Nayak, C. Physical Review Letters, Vol. 100, Issue 16 https://doi.org/10.1103/PhysRevLett.100.166803	journal	April 2008
Exact Quantization of the Even-Denominator Fractional Quantum Hall State at $ν = 5 / 2$ Landau Level Filling Factor Pan, W.; Xia, J. -S.; Shvarts, V. Physical Review Letters, Vol. 83, Issue 17 https://doi.org/10.1103/PhysRevLett.83.3530	journal	October 1999
Nonabelions in the fractional quantum hall effect Moore, Gregory; Read, Nicholas Nuclear Physics B, Vol. 360, Issue 2-3 https://doi.org/10.1016/0550-3213(91)90407-O	journal	August 1991
Spin polarization of the $ν = 12 / 5$ fractional quantum Hall state Zhang, Chi; Huan, Chao; Xia, J. S. Physical Review B, Vol. 85, Issue 24 https://doi.org/10.1103/PhysRevB.85.241302	journal	June 2012
Competing Topological Orders in the $ν = 12 / 5$ Quantum Hall State Bonderson, Parsa; Feiguin, Adrian E.; Möller, Gunnar Physical Review Letters, Vol. 108, Issue 3 https://doi.org/10.1103/PhysRevLett.108.036806	journal	January 2012
Observation of an even-denominator quantum number in the fractional quantum Hall effect Willett, R.; Eisenstein, J. P.; Störmer, H. L. Physical Review Letters, Vol. 59, Issue 15 https://doi.org/10.1103/PhysRevLett.59.1776	journal	October 1987
Observation of a quarter of an electron charge at the ν = 5/2 quantum Hall state Dolev, M.; Heiblum, M.; Umansky, V. Nature, Vol. 452, Issue 7189 https://doi.org/10.1038/nature06855	journal	April 2008
Two-Dimensional Magnetotransport in the Extreme Quantum Limit Tsui, D. C.; Stormer, H. L.; Gossard, A. C. Physical Review Letters, Vol. 48, Issue 22 https://doi.org/10.1103/PhysRevLett.48.1559	journal	May 1982
Disentangling Entanglement Spectra of Fractional Quantum Hall States on Torus Geometries Läuchli, Andreas M.; Bergholtz, Emil J.; Suorsa, Juha Physical Review Letters, Vol. 104, Issue 15 https://doi.org/10.1103/PhysRevLett.104.156404	journal	April 2010
Anomalous Quantum Hall Effect: An Incompressible Quantum Fluid with Fractionally Charged Excitations Laughlin, R. B. Physical Review Letters, Vol. 50, Issue 18 https://doi.org/10.1103/PhysRevLett.50.1395	journal	May 1983
Nonconventional Odd-Denominator Fractional Quantum Hall States in the Second Landau Level Kumar, A.; Csáthy, G. A.; Manfra, M. J. Physical Review Letters, Vol. 105, Issue 24 https://doi.org/10.1103/PhysRevLett.105.246808	journal	December 2010
Finite-Size Studies of the Incompressible State of the Fractionally Quantized Hall Effect and its Excitations Haldane, F. D. M.; Rezayi, E. H. Physical Review Letters, Vol. 54, Issue 3 https://doi.org/10.1103/PhysRevLett.54.237	journal	January 1985
Fractional Quantum Hall State at $ν = \frac{5}{2}$ and the Moore-Read Pfaffian Storni, M.; Morf, R. H.; Das Sarma, S. Physical Review Letters, Vol. 104, Issue 7 https://doi.org/10.1103/PhysRevLett.104.076803	journal	February 2010
Phase Diagram of the $ν = 5 / 2$ Fractional Quantum Hall Effect: Effects of Landau-Level Mixing and Nonzero Width Pakrouski, Kiryl; Peterson, Michael R.; Jolicoeur, Thierry Physical Review X, Vol. 5, Issue 2 https://doi.org/10.1103/PhysRevX.5.021004	journal	April 2015
Model Fractional Quantum Hall States and Jack Polynomials Bernevig, B. Andrei; Haldane, F. D. M. Physical Review Letters, Vol. 100, Issue 24 https://doi.org/10.1103/PhysRevLett.100.246802	journal	June 2008
Comparison of the density-matrix renormalization group method applied to fractional quantum Hall systems in different geometries Hu, Zi-Xiang; Papić, Z.; Johri, S. Physics Letters A, Vol. 376, Issue 30-31 https://doi.org/10.1016/j.physleta.2012.05.031	journal	June 2012
Topological Entanglement in Abelian and Non-Abelian Excitation Eigenstates Papić, Z.; Bernevig, B. A.; Regnault, N. Physical Review Letters, Vol. 106, Issue 5 https://doi.org/10.1103/PhysRevLett.106.056801	journal	February 2011
Even-denominator fractional quantum Hall physics in ZnO Falson, J.; Maryenko, D.; Friess, B. Nature Physics, Vol. 11, Issue 4 https://doi.org/10.1038/nphys3259	journal	March 2015
Braid Topologies for Quantum Computation Bonesteel, N. E.; Hormozi, L.; Zikos, G. Physical Review Letters, Vol. 95, Issue 14 https://doi.org/10.1103/PhysRevLett.95.140503	journal	September 2005
A Modular Functor Which is Universal¶for Quantum Computation Freedman, Michael H.; Larsen, Michael; Wang, Zhenghan Communications in Mathematical Physics, Vol. 227, Issue 3 https://doi.org/10.1007/s002200200645	journal	June 2002
Topological Orders in Rigid States Wen, X. G. International Journal of Modern Physics B, Vol. 04, Issue 02 https://doi.org/10.1142/S0217979290000139	journal	February 1990
Composite Fermions Jain, Jainendra K. https://doi.org/10.1017/CBO9780511607561	book	January 2007
Correlation Lengths and Topological Entanglement Entropies of Unitary and Nonunitary Fractional Quantum Hall Wave Functions Estienne, B.; Regnault, N.; Bernevig, B. A. Physical Review Letters, Vol. 114, Issue 18 https://doi.org/10.1103/PhysRevLett.114.186801	journal	May 2015
Infinite density matrix renormalization group for multicomponent quantum Hall systems Zaletel, Michael P.; Mong, Roger S. K.; Pollmann, Frank Physical Review B, Vol. 91, Issue 4 https://doi.org/10.1103/PhysRevB.91.045115	journal	January 2015
Bipartite entanglement entropy in fractional quantum Hall states Zozulya, O. S.; Haque, M.; Schoutens, K. Physical Review B, Vol. 76, Issue 12 https://doi.org/10.1103/PhysRevB.76.125310	journal	September 2007
Model Wave Functions for the Collective Modes and the Magnetoroton Theory of the Fractional Quantum Hall Effect Yang, Bo; Hu, Zi-Xiang; Papić, Z. Physical Review Letters, Vol. 108, Issue 25 https://doi.org/10.1103/PhysRevLett.108.256807	journal	June 2012
Experimental probe of topological orders and edge excitations in the second Landau level Baer, S.; Rössler, C.; Ihn, T. Physical Review B, Vol. 90, Issue 7 https://doi.org/10.1103/PhysRevB.90.075403	journal	August 2014
Non-Abelian anyons and topological quantum computation Nayak, Chetan; Simon, Steven H.; Stern, Ady Reviews of Modern Physics, Vol. 80, Issue 3 https://doi.org/10.1103/RevModPhys.80.1083	journal	September 2008
Orbital Landau level dependence of the fractional quantum Hall effect in quasi-two-dimensional electron layers: Finite-thickness effects Peterson, Michael R.; Jolicoeur, Th.; Das Sarma, S. Physical Review B, Vol. 78, Issue 15 https://doi.org/10.1103/PhysRevB.78.155308	journal	October 2008
Fault-tolerant quantum computation by anyons Kitaev, A. Yu. Annals of Physics, Vol. 303, Issue 1 https://doi.org/10.1016/S0003-4916(02)00018-0	journal	January 2003
Characterizing Topological Order by Studying the Ground States on an Infinite Cylinder Cincio, L.; Vidal, G. Physical Review Letters, Vol. 110, Issue 6 https://doi.org/10.1103/PhysRevLett.110.067208	journal	February 2013
Collective-Excitation Gap in the Fractional Quantum Hall Effect Girvin, S. M.; MacDonald, A. H.; Platzman, P. M. Physical Review Letters, Vol. 54, Issue 6 https://doi.org/10.1103/PhysRevLett.54.581	journal	February 1985
Experimental studies of the fractional quantum Hall effect in the first excited Landau level Pan, W.; Xia, J. S.; Stormer, H. L. Physical Review B, Vol. 77, Issue 7 https://doi.org/10.1103/PhysRevB.77.075307	journal	February 2008
Tripartite composite fermion states Sreejith, G. J.; Wu, Ying-Hai; Wójs, A. Physical Review B, Vol. 87, Issue 24 https://doi.org/10.1103/PhysRevB.87.245125	journal	June 2013
Entanglement measures for quasi-two-dimensional fractional quantum Hall states Biddle, J.; Peterson, Michael R.; Das Sarma, S. Physical Review B, Vol. 84, Issue 12 https://doi.org/10.1103/PhysRevB.84.125141	journal	September 2011
Landau level quantization on the sphere Greiter, Martin Physical Review B, Vol. 83, Issue 11 https://doi.org/10.1103/PhysRevB.83.115129	journal	March 2011
Generalized clustering conditions of Jack polynomials at negative Jack parameter $α$ Bernevig, B. Andrei; Haldane, F. D. M. Physical Review B, Vol. 77, Issue 18 https://doi.org/10.1103/PhysRevB.77.184502	journal	May 2008
Non-Abelian quantized Hall states of electrons at filling factors 12/5 and 13/5 in the first excited Landau level Rezayi, E. H.; Read, N. Physical Review B, Vol. 79, Issue 7 https://doi.org/10.1103/PhysRevB.79.075306	journal	February 2009

Similar Records

Spin polarization of the

ν = 12 / 5

fractional quantum Hall state

Journal Article · Thu Jun 07 00:00:00 EDT 2012 · Physical Review B · OSTI ID:1221702

Zhang, Chi; Huan, Chao; Xia, J. S.; +6 more

Non-Abelian phases in two-component

ν = 2 / 3

fractional quantum Hall states: Emergence of Fibonacci anyons

Journal Article · Wed Aug 05 00:00:00 EDT 2015 · Physical Review B · OSTI ID:1221702

Liu, Zhao; Vaezi, Abolhassan; Lee, Kyungmin; +1 more

Fabry-Pérot Interferometry at the

ν = 2 / 5

Fractional Quantum Hall State

Journal Article · Mon Oct 23 00:00:00 EDT 2023 · Physical Review. X · OSTI ID:1221702

Nakamura, J.; Liang, S.; Gardner, G. C.; +1 more

Title: Fractional Quantum Hall States at ν = 13 / 5 and 12 / 5 and Their Non-Abelian Nature

Citation Formats

References (68)

Similar Records

Related Subjects

Title: Fractional Quantum Hall States at $ν = 13 / 5$ and $12 / 5$ and Their Non-Abelian Nature