DisorderDriven Transition in the $\nu =5/2$ Fractional Quantum Hall Effect
Abstract
The fractional quantum Hall (FQH) effect at the filling number ν = 5/2 is a primary candidate for nonAbelian topological order, while the fate of such a state in the presence of random disorder has not been resolved. We address this open question by implementing an unbiased diagnosis based on numerical exact diagonalization. Here, we calculate the disorder averaged Hall conductance and the associated statistical distribution of the topological invariant Chern number, which unambiguously characterize the disorderdriven collapse of the FQH state. As the disorder strength increases towards a critical value, a continuous phase transition is detected based on the disorder configuration averaged wave function fidelity and the entanglement entropy. In the strong disorder regime, we identify a composite Fermi liquid phase with fluctuating Chern numbers, in striking contrast to the wellknown ν = 1/3 case where an Anderson insulator appears. Interestingly, the lowest Landau level projected a local density profile, the wave function overlap, and the entanglement entropy as a function of disorder strength simultaneously signal an intermediate phase, which may be relevant to the recent proposal of a particlehole Pfaffian state or Pfaffian–antiPfaffian puddle state.
 Authors:

 Westlake Univ., Hangzhou (China); Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
 California State Univ., Northridge, CA (United States)
 Publication Date:
 Research Org.:
 Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
 Sponsoring Org.:
 USDOE
 OSTI Identifier:
 1571593
 Alternate Identifier(s):
 OSTI ID: 1546824
 Report Number(s):
 LAUR1828368
Journal ID: ISSN 00319007; PRLTAO; TRN: US2100185
 Grant/Contract Number:
 89233218CNA000001
 Resource Type:
 Accepted Manuscript
 Journal Name:
 Physical Review Letters
 Additional Journal Information:
 Journal Volume: 123; Journal Issue: 5; Journal ID: ISSN 00319007
 Publisher:
 American Physical Society (APS)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 36 MATERIALS SCIENCE; Material Science
Citation Formats
Zhu, Wei, and Sheng, D. N. DisorderDriven Transition in the ν=5/2 Fractional Quantum Hall Effect. United States: N. p., 2019.
Web. doi:10.1103/PhysRevLett.123.056804.
Zhu, Wei, & Sheng, D. N. DisorderDriven Transition in the ν=5/2 Fractional Quantum Hall Effect. United States. doi:10.1103/PhysRevLett.123.056804.
Zhu, Wei, and Sheng, D. N. Thu .
"DisorderDriven Transition in the ν=5/2 Fractional Quantum Hall Effect". United States. doi:10.1103/PhysRevLett.123.056804. https://www.osti.gov/servlets/purl/1571593.
@article{osti_1571593,
title = {DisorderDriven Transition in the ν=5/2 Fractional Quantum Hall Effect},
author = {Zhu, Wei and Sheng, D. N.},
abstractNote = {The fractional quantum Hall (FQH) effect at the filling number ν = 5/2 is a primary candidate for nonAbelian topological order, while the fate of such a state in the presence of random disorder has not been resolved. We address this open question by implementing an unbiased diagnosis based on numerical exact diagonalization. Here, we calculate the disorder averaged Hall conductance and the associated statistical distribution of the topological invariant Chern number, which unambiguously characterize the disorderdriven collapse of the FQH state. As the disorder strength increases towards a critical value, a continuous phase transition is detected based on the disorder configuration averaged wave function fidelity and the entanglement entropy. In the strong disorder regime, we identify a composite Fermi liquid phase with fluctuating Chern numbers, in striking contrast to the wellknown ν = 1/3 case where an Anderson insulator appears. Interestingly, the lowest Landau level projected a local density profile, the wave function overlap, and the entanglement entropy as a function of disorder strength simultaneously signal an intermediate phase, which may be relevant to the recent proposal of a particlehole Pfaffian state or Pfaffian–antiPfaffian puddle state.},
doi = {10.1103/PhysRevLett.123.056804},
journal = {Physical Review Letters},
number = 5,
volume = 123,
place = {United States},
year = {2019},
month = {8}
}
Web of Science
Works referenced in this record:
Parton construction of a wave function in the antiPfaffian phase
journal, July 2018
 Balram, Ajit C.; Barkeshli, Maissam; Rudner, Mark S.
 Physical Review B, Vol. 98, Issue 3
Particlehole symmetry breaking and the $\nu ={\scriptstyle \frac{5}{2}}$ fractional quantum Hall effect
journal, December 2009
 Wang, Hao; Sheng, D. N.; Haldane, F. D. M.
 Physical Review B, Vol. 80, Issue 24
Is the Composite Fermion a Dirac Particle?
journal, September 2015
 Son, Dam Thanh
 Physical Review X, Vol. 5, Issue 3
Entanglement scaling of fractional quantum Hall states through geometric deformations
journal, July 2010
 Läuchli, Andreas M.; Bergholtz, Emil J.; Haque, Masudul
 New Journal of Physics, Vol. 12, Issue 7
Fractional quantum Hall states at $\frac{1}{3}$ and $\frac{5}{2}$ filling: Densitymatrix renormalization group calculations
journal, May 2011
 Zhao, Jize; Sheng, D. N.; Haldane, F. D. M.
 Physical Review B, Vol. 83, Issue 19
Theory of DisorderInduced HalfInteger Thermal Hall Conductance
journal, July 2018
 Mross, David F.; Oreg, Yuval; Stern, Ady
 Physical Review Letters, Vol. 121, Issue 2
Activation gaps of fractional quantum Hall effect in the second Landau level
journal, February 2008
 Choi, H. C.; Kang, W.; Das Sarma, S.
 Physical Review B, Vol. 77, Issue 8
Paired Hall state at half filling
journal, June 1991
 Greiter, Martin; Wen, XiaoGang; Wilczek, Frank
 Physical Review Letters, Vol. 66, Issue 24
Beyond paired quantum Hall states: Parafermions and incompressible states in the first excited Landau level
journal, March 1999
 Read, N.; Rezayi, E.
 Physical Review B, Vol. 59, Issue 12
Observation of neutral modes in the fractional quantum Hall regime
journal, July 2010
 Bid, Aveek; Ofek, N.; Inoue, H.
 Nature, Vol. 466, Issue 7306
Numerical exploration of trial wave functions for the particleholesymmetric Pfaffian
journal, August 2018
 Mishmash, Ryan V.; Mross, David F.; Alicea, Jason
 Physical Review B, Vol. 98, Issue 8
Evolution of quantum entanglement with disorder in fractional quantum Hall liquids
journal, September 2017
 Liu, Zhao; Bhatt, R. N.
 Physical Review B, Vol. 96, Issue 11
QuasiParticle Properties from Tunneling in the Formula Fractional Quantum Hall State
journal, May 2008
 Radu, I. P.; Miller, J. B.; Marcus, C. M.
 Science, Vol. 320, Issue 5878
Quantum Entanglement as a Diagnostic of Phase Transitions in Disordered Fractional Quantum Hall Liquids
journal, November 2016
 Liu, Zhao; Bhatt, R. N.
 Physical Review Letters, Vol. 117, Issue 20
Universal conductance in the lowest Landau level
journal, January 1993
 Huo, Y.; Hetzel, R. E.; Bhatt, R. N.
 Physical Review Letters, Vol. 70, Issue 4
Detecting Topological Order in a Ground State Wave Function
journal, March 2006
 Levin, Michael; Wen, XiaoGang
 Physical Review Letters, Vol. 96, Issue 11
Entanglement in manybody systems
journal, May 2008
 Amico, Luigi; Fazio, Rosario; Osterloh, Andreas
 Reviews of Modern Physics, Vol. 80, Issue 2
Insulating and Fractional Quantum Hall States in the First Excited Landau Level
journal, January 2002
 Eisenstein, J. P.; Cooper, K. B.; Pfeiffer, L. N.
 Physical Review Letters, Vol. 88, Issue 7
Topological Entanglement Entropy
journal, March 2006
 Kitaev, Alexei; Preskill, John
 Physical Review Letters, Vol. 96, Issue 11
Theory of the halffilled Landau level
journal, March 1993
 Halperin, B. I.; Lee, Patrick A.; Read, Nicholas
 Physical Review B, Vol. 47, Issue 12
ParticleHole Symmetry and the Pfaffian State
journal, December 2007
 Levin, Michael; Halperin, Bertrand I.; Rosenow, Bernd
 Physical Review Letters, Vol. 99, Issue 23
Landau Level Mixing and the Ground State of the $\nu =5/2$ Quantum Hall Effect
journal, July 2017
 Rezayi, Edward H.
 Physical Review Letters, Vol. 119, Issue 2
Entanglement Entropy in Fermionic Laughlin States
journal, February 2007
 Haque, Masudul; Zozulya, Oleksandr; Schoutens, Kareljan
 Physical Review Letters, Vol. 98, Issue 6
ParticleHole Symmetry and the $\nu =\frac{5}{2}$ Quantum Hall State
journal, December 2007
 Lee, SungSik; Ryu, Shinsei; Nayak, Chetan
 Physical Review Letters, Vol. 99, Issue 23
Impurity Scattering in Carbon Nanotubes – Absence of Back Scattering –
journal, May 1998
 Ando, Tsuneya; Nakanishi, Takeshi
 Journal of the Physical Society of Japan, Vol. 67, Issue 5
Striped quantum Hall state in a halffilled Landau level
journal, May 2016
 Wan, Xin; Yang, Kun
 Physical Review B, Vol. 93, Issue 20
Measurement of filling factor 5/2 quasiparticle interference with observation of charge e/4 and e/2 period oscillations
journal, May 2009
 Willett, R. L.; Pfeiffer, L. N.; West, K. W.
 Proceedings of the National Academy of Sciences, Vol. 106, Issue 22
Topological order from disorder and the quantized Hall thermal metal: Possible applications to the $\nu =5/2$ state
journal, July 2018
 Wang, Chong; Vishwanath, Ashvin; Halperin, Bertrand I.
 Physical Review B, Vol. 98, Issue 4
$\nu =5/2$ Fractional Quantum Hall State in the Presence of Alloy Disorder
journal, March 2014
 Deng, Nianpei; Gardner, G. C.; Mondal, S.
 Physical Review Letters, Vol. 112, Issue 11
Impact of Disorder on the $5/2$ Fractional Quantum Hall State
journal, May 2011
 Pan, W.; Masuhara, N.; Sullivan, N. S.
 Physical Review Letters, Vol. 106, Issue 20
Density Matrix Renormalization Group Study of Incompressible Fractional Quantum Hall States
journal, April 2008
 Feiguin, A. E.; Rezayi, E.; Nayak, C.
 Physical Review Letters, Vol. 100, Issue 16
Exact Quantization of the EvenDenominator Fractional Quantum Hall State at $\mathit{\nu}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}5\mathrm{}/2$ Landau Level Filling Factor
journal, October 1999
 Pan, W.; Xia, J. S.; Shvarts, V.
 Physical Review Letters, Vol. 83, Issue 17
A Topological Look at the Quantum Hall Effect
journal, August 2003
 Avron, Joseph E.; Osadchy, Daniel; Seiler, Ruedi
 Physics Today, Vol. 56, Issue 8
Fractional quantum Hall bilayers at half filling: Tunnelingdriven nonAbelian phase
journal, December 2016
 Zhu, W.; Liu, Zhao; Haldane, F. D. M.
 Physical Review B, Vol. 94, Issue 24
Berry Phase and Model Wave Function in the HalfFilled Landau Level
journal, October 2018
 Geraedts, Scott D.; Wang, Jie; Rezayi, E. H.
 Physical Review Letters, Vol. 121, Issue 14
Role of disorder in halffilled high Landau levels
journal, October 2002
 Sheng, D. N.; Wang, Ziqiang; Friedman, B.
 Physical Review B, Vol. 66, Issue 16
Nonabelions in the fractional quantum hall effect
journal, August 1991
 Moore, Gregory; Read, Nicholas
 Nuclear Physics B, Vol. 360, Issue 23
Observation of an evendenominator quantum number in the fractional quantum Hall effect
journal, October 1987
 Willett, R.; Eisenstein, J. P.; Störmer, H. L.
 Physical Review Letters, Vol. 59, Issue 15
Observation of a quarter of an electron charge at the ν = 5/2 quantum Hall state
journal, April 2008
 Dolev, M.; Heiblum, M.; Umansky, V.
 Nature, Vol. 452, Issue 7189
TwoDimensional Magnetotransport in the Extreme Quantum Limit
journal, May 1982
 Tsui, D. C.; Stormer, H. L.; Gossard, A. C.
 Physical Review Letters, Vol. 48, Issue 22
Theory of the disordered $\nu =\frac{5}{2}$ quantum thermal Hall state: Emergent symmetry and phase diagram
journal, April 2018
 Lian, Biao; Wang, Juven
 Physical Review B, Vol. 97, Issue 16
Anomalous Quantum Hall Effect: An Incompressible Quantum Fluid with Fractionally Charged Excitations
journal, May 1983
 Laughlin, R. B.
 Physical Review Letters, Vol. 50, Issue 18
Colloquium : Area laws for the entanglement entropy
journal, February 2010
 Eisert, J.; Cramer, M.; Plenio, M. B.
 Reviews of Modern Physics, Vol. 82, Issue 1
Fractional Quantum Hall State at $\nu =\frac{5}{2}$ and the MooreRead Pfaffian
journal, February 2010
 Storni, M.; Morf, R. H.; Das Sarma, S.
 Physical Review Letters, Vol. 104, Issue 7
Nonconventional OddDenominator Fractional Quantum Hall States in the Second Landau Level
journal, December 2010
 Kumar, A.; Csáthy, G. A.; Manfra, M. J.
 Physical Review Letters, Vol. 105, Issue 24
Transition from Quantum Hall to Compressible States in the Second Landau Level: New Light on the $\nu \phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}5\mathrm{}/2$ Enigma
journal, February 1998
 Morf, R. H.
 Physical Review Letters, Vol. 80, Issue 7
Spontaneous ParticleHole Symmetry Breaking in the $\nu =5/2$ Fractional Quantum Hall Effect
journal, October 2008
 Peterson, Michael R.; Park, Kwon; Das Sarma, S.
 Physical Review Letters, Vol. 101, Issue 15
Phase Diagram of the $\nu =5/2$ Fractional Quantum Hall Effect: Effects of LandauLevel Mixing and Nonzero Width
journal, April 2015
 Pakrouski, Kiryl; Peterson, Michael R.; Jolicoeur, Thierry
 Physical Review X, Vol. 5, Issue 2
Quantized Hall Conductance in a TwoDimensional Periodic Potential
journal, August 1982
 Thouless, D. J.; Kohmoto, M.; Nightingale, M. P.
 Physical Review Letters, Vol. 49, Issue 6
Incompressible Paired Hall State, Stripe Order, and the Composite Fermion Liquid Phase in HalfFilled Landau Levels
journal, May 2000
 Rezayi, E. H.; Haldane, F. D. M.
 Physical Review Letters, Vol. 84, Issue 20
The halffilled Landau level: The case for Dirac composite fermions
journal, April 2016
 Geraedts, S. D.; Zaletel, M. P.; Mong, R. S. K.
 Science, Vol. 352, Issue 6282
Density dependence of the $\nu ={\scriptstyle \frac{5}{2}}$ energy gap: Experiment and theory
journal, January 2010
 Nuebler, J.; Umansky, V.; Morf, R.
 Physical Review B, Vol. 81, Issue 3
MagneticFieldTuned AharonovBohm Oscillations and Evidence for NonAbelian Anyons at $\nu =5/2$
journal, October 2013
 Willett, R. L.; Nayak, C.; Shtengel, K.
 Physical Review Letters, Vol. 111, Issue 18
Quantized Hall conductance as a topological invariant
journal, March 1985
 Niu, Qian; Thouless, D. J.; Wu, YongShi
 Physical Review B, Vol. 31, Issue 6
Topological Delocalization of TwoDimensional Massless Dirac Fermions
journal, October 2007
 Nomura, Kentaro; Koshino, Mikito; Ryu, Shinsei
 Physical Review Letters, Vol. 99, Issue 14
Stabilization of the ParticleHole Pfaffian Order by LandauLevel Mixing and Impurities That Break ParticleHole Symmetry
journal, August 2016
 Zucker, P. T.; Feldman, D. E.
 Physical Review Letters, Vol. 117, Issue 9
Topological Orders in Rigid States
journal, February 1990
 Wen, X. G.
 International Journal of Modern Physics B, Vol. 04, Issue 02
Spontaneous Breakdown of Translational Symmetry in Quantum Hall Systems: Crystalline Order in High Landau Levels
journal, December 2000
 Haldane, F. D. M.; Rezayi, E. H.; Yang, Kun
 Physical Review Letters, Vol. 85, Issue 25
Infinite density matrix renormalization group for multicomponent quantum Hall systems
journal, January 2015
 Zaletel, Michael P.; Mong, Roger S. K.; Pollmann, Frank
 Physical Review B, Vol. 91, Issue 4
Mobility gap in fractional quantum Hall liquids: Effects of disorder and layer thickness
journal, August 2005
 Wan, Xin; Sheng, D. N.; Rezayi, E. H.
 Physical Review B, Vol. 72, Issue 7
Symmetry enforced nonAbelian topological order at the surface of a topological insulator
journal, April 2014
 Chen, Xie; Fidkowski, Lukasz; Vishwanath, Ashvin
 Physical Review B, Vol. 89, Issue 16
NonAbelian anyons and topological quantum computation
journal, September 2008
 Nayak, Chetan; Simon, Steven H.; Stern, Ady
 Reviews of Modern Physics, Vol. 80, Issue 3
Paired states in halffilled Landau levels
journal, June 2017
 Milovanović, M. V.
 Physical Review B, Vol. 95, Issue 23
DisorderDriven Collapse of the Mobility Gap and Transition to an Insulator in the Fractional Quantum Hall Effect
journal, June 2003
 Sheng, D. N.; Wan, Xin; Rezayi, E. H.
 Physical Review Letters, Vol. 90, Issue 25
Localization, wavefunction topology, and the integer quantized Hall effect
journal, February 1988
 Arovas, Daniel P.; Bhatt, R. N.; Haldane, F. D. M.
 Physical Review Letters, Vol. 60, Issue 7
Faulttolerant quantum computation by anyons
journal, January 2003
 Kitaev, A. Yu.
 Annals of Physics, Vol. 303, Issue 1
Paired states of fermions in two dimensions with breaking of parity and timereversal symmetries and the fractional quantum Hall effect
journal, April 2000
 Read, N.; Green, Dmitry
 Physical Review B, Vol. 61, Issue 15
Topological invariant and the quantization of the Hall conductance
journal, April 1985
 Kohmoto, Mahito
 Annals of Physics, Vol. 160, Issue 2
Breaking of ParticleHole Symmetry by Landau Level Mixing in the $\nu =5/2$ Quantized Hall State
journal, March 2011
 Rezayi, Edward H.; Simon, Steven H.
 Physical Review Letters, Vol. 106, Issue 11
Chern number and edge states in the integer quantum Hall effect
journal, November 1993
 Hatsugai, Yasuhiro
 Physical Review Letters, Vol. 71, Issue 22
Berry Curvature on the Fermi Surface: Anomalous Hall Effect as a Topological FermiLiquid Property
journal, November 2004
 Haldane, F. D. M.
 Physical Review Letters, Vol. 93, Issue 20
$\nu =5/2$ fractional quantum Hall state in lowmobility electron systems: Different roles of disorder
journal, August 2013
 Gamez, Gerardo; Muraki, Koji
 Physical Review B, Vol. 88, Issue 7
Quantum entanglement in condensed matter systems
journal, August 2016
 Laflorencie, Nicolas
 Physics Reports, Vol. 646
Experimental studies of the fractional quantum Hall effect in the first excited Landau level
journal, February 2008
 Pan, W.; Xia, J. S.; Stormer, H. L.
 Physical Review B, Vol. 77, Issue 7
Observation of halfinteger thermal Hall conductance
journal, June 2018
 Banerjee, Mitali; Heiblum, Moty; Umansky, Vladimir
 Nature, Vol. 559, Issue 7713
Particlehole symmetry in the anomalous quantum Hall effect
journal, May 1984
 Girvin, S. M.
 Physical Review B, Vol. 29, Issue 10
ChargeDensityWave Ordering in HalfFilled High Landau Levels
journal, August 1999
 Rezayi, E. H.; Haldane, F. D. M.; Yang, Kun
 Physical Review Letters, Vol. 83, Issue 6