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Title: Disorder-Driven Transition in the ν = 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 non-Abelian 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 disorder-driven 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 well-known 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 particle-hole Pfaffian state or Pfaffian–anti-Pfaffian puddle state.

Authors:
ORCiD logo [1];  [2]
  1. Westlake Univ., Hangzhou (China); Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
  2. 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):
LA-UR-18-28368
Journal ID: ISSN 0031-9007; PRLTAO
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 0031-9007
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. Disorder-Driven 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. Disorder-Driven 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 . "Disorder-Driven Transition in the ν=5/2 Fractional Quantum Hall Effect". United States. doi:10.1103/PhysRevLett.123.056804.
@article{osti_1571593,
title = {Disorder-Driven 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 non-Abelian 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 disorder-driven 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 well-known 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 particle-hole Pfaffian state or Pfaffian–anti-Pfaffian puddle state.},
doi = {10.1103/PhysRevLett.123.056804},
journal = {Physical Review Letters},
number = 5,
volume = 123,
place = {United States},
year = {2019},
month = {8}
}

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