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Title: Surprising robustness of particle-hole symmetry for composite-fermion liquids

Abstract

Here, we report on fixed phase diffusion Monte Carlo calculations that show that, even for a large amount of Landau level mixing, the energies of the Pfaffian and anti-Pfaffian phases remain very nearly the same, as also do the excitation gaps at 1/3 and 2/3. These results, combined with previous theoretical and experimental investigations, indicate that particle hole (PH) symmetry for composite fermion states is much more robust than a priori expected, emerging even in models that explicitly break PH symmetry. We provide insight into this fact by showing that the low energy physics of a generic repulsive 3-body interaction is captured, to a large extent and over a range of filling factors, by a mean field approximation that maps it into a PH symmetric 2-body interaction. This explains why Landau level mixing, which effectively generates such a generic 3-body interaction, is inefficient in breaking PH symmetry. As a byproduct, our results provide a systematic construction of a 2-body interaction which produces, to a good approximation, the Pfaffian wave function as its ground state.

Authors:
 [1];  [2];  [2]
  1. Indian Institute of Science Education and Research, Pune (India)
  2. Pennsylvania State Univ., University Park, PA (United States)
Publication Date:
Research Org.:
Pennsylvania State Univ., University Park, PA (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22)
OSTI Identifier:
1489114
Alternate Identifier(s):
OSTI ID: 1394708
Grant/Contract Number:  
SC0005042
Resource Type:
Accepted Manuscript
Journal Name:
Physical Review B
Additional Journal Information:
Journal Volume: 96; Journal Issue: 12; Journal ID: ISSN 2469-9950
Publisher:
American Physical Society (APS)
Country of Publication:
United States
Language:
English
Subject:
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; fractional quantum Hall effect; composite fermions; emergent symmetry

Citation Formats

Sreejith, G. J., Zhang, Yuhe, and Jain, J. K. Surprising robustness of particle-hole symmetry for composite-fermion liquids. United States: N. p., 2017. Web. doi:10.1103/PhysRevB.96.125149.
Sreejith, G. J., Zhang, Yuhe, & Jain, J. K. Surprising robustness of particle-hole symmetry for composite-fermion liquids. United States. doi:10.1103/PhysRevB.96.125149.
Sreejith, G. J., Zhang, Yuhe, and Jain, J. K. Mon . "Surprising robustness of particle-hole symmetry for composite-fermion liquids". United States. doi:10.1103/PhysRevB.96.125149. https://www.osti.gov/servlets/purl/1489114.
@article{osti_1489114,
title = {Surprising robustness of particle-hole symmetry for composite-fermion liquids},
author = {Sreejith, G. J. and Zhang, Yuhe and Jain, J. K.},
abstractNote = {Here, we report on fixed phase diffusion Monte Carlo calculations that show that, even for a large amount of Landau level mixing, the energies of the Pfaffian and anti-Pfaffian phases remain very nearly the same, as also do the excitation gaps at 1/3 and 2/3. These results, combined with previous theoretical and experimental investigations, indicate that particle hole (PH) symmetry for composite fermion states is much more robust than a priori expected, emerging even in models that explicitly break PH symmetry. We provide insight into this fact by showing that the low energy physics of a generic repulsive 3-body interaction is captured, to a large extent and over a range of filling factors, by a mean field approximation that maps it into a PH symmetric 2-body interaction. This explains why Landau level mixing, which effectively generates such a generic 3-body interaction, is inefficient in breaking PH symmetry. As a byproduct, our results provide a systematic construction of a 2-body interaction which produces, to a good approximation, the Pfaffian wave function as its ground state.},
doi = {10.1103/PhysRevB.96.125149},
journal = {Physical Review B},
number = 12,
volume = 96,
place = {United States},
year = {2017},
month = {9}
}

Journal Article:
Free Publicly Available Full Text
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Cited by: 6 works
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Figures / Tables:

FIG. 1. FIG. 1.: (a) The DMC energies for Pfaffian and anti-Pfaffian states at ν = 5/2 as a function of κ for ideal 2D system (w = 0), obtained from extrapolation from systems with up to 32 and 30 particles, respectively. (b) The energies for spin polarized (SP) states at νmore » = 3/2 for w = 0 and quantum wells of width w = 30nm and 50nm (obtained from extrapolation of energies of up to 20 and 18 particles). All energies shown are obtained by extrapolating finite-system results to thermodynamic limit with the error bars indicating the extrapolation errors.« less

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Works referenced in this record:

Decomposition of fractional quantum Hall model states: Product rule symmetries and approximations
journal, July 2011


Construction of edge states in fractional quantum Hall systems by Jack polynomials
journal, April 2014


Is the Composite Fermion a Dirac Particle?
journal, September 2015


New stochastic method for systems with broken time-reversal symmetry: 2D fermions in a magnetic field
journal, October 1993


Paired Hall states
journal, May 1992


Global Phase Diagram of the Fractional Quantum Hall Effect Arising from Repulsive Three-Body Interactions
journal, November 2010


What Determines the Fermi Wave Vector of Composite Fermions?
journal, November 2014


Quantum Hall Fluids on the Haldane Sphere: A Diffusion Monte Carlo Study
journal, December 1997


Phase Diagram of the ν = 5 / 2 Fractional Quantum Hall Effect: Effects of Landau-Level Mixing and Nonzero Width
journal, April 2015

  • Pakrouski, Kiryl; Peterson, Michael R.; Jolicoeur, Thierry
  • Physical Review X, Vol. 5, Issue 2
  • DOI: 10.1103/PhysRevX.5.021004

Spontaneous Particle-Hole Symmetry Breaking in the ν = 5 / 2 Fractional Quantum Hall Effect
journal, October 2008


Nature of composite fermions and the role of particle-hole symmetry: A microscopic account
journal, June 2016


Model Fractional Quantum Hall States and Jack Polynomials
journal, June 2008


Fractional Quantization of the Hall Effect: A Hierarchy of Incompressible Quantum Fluid States
journal, August 1983


Quantum Monte Carlo simulations of solids
journal, January 2001


The half-filled Landau level: The case for Dirac composite fermions
journal, April 2016


Maximum-density droplet to lower-density droplet transition in quantum dots
journal, July 2005


Fixed‐node quantum Monte Carlo for molecules a) b)
journal, December 1982

  • Reynolds, Peter J.; Ceperley, David M.; Alder, Berni J.
  • The Journal of Chemical Physics, Vol. 77, Issue 11
  • DOI: 10.1063/1.443766

Generalized quantum Hall projection Hamiltonians
journal, February 2007


Construction of a paired wave function for spinless electrons at filling fraction ν = 2 5
journal, February 2007


Transference of Fermi Contour Anisotropy to Composite Fermions
journal, July 2017


Infinite density matrix renormalization group for multicomponent quantum Hall systems
journal, January 2015


Landau-Level Mixing and the Emergence of Pfaffian Excitations for the 5 / 2 Fractional Quantum Hall Effect
journal, August 2010


Bipartite Composite Fermion States
journal, August 2011


Anatomy of Abelian and Non-Abelian Fractional Quantum Hall States
journal, November 2009


Composite fermions and Landau-level mixing in the fractional quantum Hall effect
journal, December 1995


Particle-Hole Symmetry and the Pfaffian State
journal, December 2007


Landau Level Mixing and the Ground State of the ν = 5 / 2 Quantum Hall Effect
journal, July 2017


Half-filled Landau level, topological insulator surfaces, and three-dimensional quantum spin liquids
journal, February 2016


Unpaired Composite Fermion, Topological Exciton, and Zero Mode
journal, September 2011


Particle-Hole Symmetry and the ν = 5 2 Quantum Hall State
journal, December 2007


Breaking of Particle-Hole Symmetry by Landau Level Mixing in the ν = 5 / 2 Quantized Hall State
journal, March 2011


Effect of Landau level mixing on the effective interaction between electrons in the fractional quantum Hall regime
journal, September 2009


Composite Fermi liquids in the lowest Landau level
journal, December 2016


Emergent particle-hole symmetry in spinful bosonic quantum Hall systems
journal, August 2017


Composite-fermion approach for the fractional quantum Hall effect
journal, July 1989


Landau-Level Mixing and Particle-Hole Symmetry Breaking for Spin Transitions in the Fractional Quantum Hall Effect
journal, September 2016


Nonabelions in the fractional quantum hall effect
journal, August 1991


More realistic Hamiltonians for the fractional quantum Hall regime in GaAs and graphene
journal, June 2013


Particle-Hole Symmetry in the Fermion-Chern-Simons and Dirac Descriptions of a Half-Filled Landau Level
journal, August 2017


    Figures/Tables have been extracted from DOE-funded journal article accepted manuscripts.