Composite fermion nonlinear sigma models
Abstract
We study particle-hole symmetry at the integer quantum Hall plateau transition using composite fermion mean-field theory. Because this theory implicitly includes some electron-electron interactions, it also has applications to certain fractional quantum Hall plateau transitions. Previous work [P. Kumar et al., Phys. Rev. B 100, 235124 (2019)] using this approach showed that the diffusive quantum criticality of this transition is described by a nonlinear sigma model with topological θ = π term. This result, which holds for both the Dirac and Halperin, Lee, and Read composite fermion theories, signifies an emergent particle-hole (reflection) symmetry of the integer (fractional) quantum Hall transition. Here we consider the stability of this result to various particle-hole symmetry-violating perturbations. In the presence of quenched disorder that preserves particle-hole symmetry, we find that finite longitudinal conductivity at this transition requires the vanishing of a symmetry-violating composite fermion effective mass, which if present would generally lead to θ ≠ π and a corresponding violation of particle-hole symmetric electrical transport σxy ≠ $$\frac1{2}$$$$\frac{e^2}{h}$$ . When the disorder does not preserve particle-hole symmetry, we find that θ can vary continuously within the diffusive regime. Our results call for further study of the universality of the quantum Hall plateau transition.
- Authors:
-
- California Institute of Technology (CalTech), Pasadena, CA (United States)
- Princeton Univ., NJ (United States)
- Univ. of California, Riverside, CA (United States)
- Publication Date:
- Research Org.:
- Princeton Univ., NJ (United States); Univ. of California, Riverside, CA (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC)
- OSTI Identifier:
- 1850797
- Grant/Contract Number:
- SC0002140; SC0020007
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Physical Review. B
- Additional Journal Information:
- Journal Volume: 104; 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; Materials Science; Physics; Composite fermions; Electrical conductivity; Fractional quantum Hall effect; Integer quantum Hall effect; Localization; Topological phase transition; Sigma models
Citation Formats
Lee, Chao-Jung, Kumar, Prashant, and Mulligan, Michael. Composite fermion nonlinear sigma models. United States: N. p., 2021.
Web. doi:10.1103/physrevb.104.125119.
Lee, Chao-Jung, Kumar, Prashant, & Mulligan, Michael. Composite fermion nonlinear sigma models. United States. https://doi.org/10.1103/physrevb.104.125119
Lee, Chao-Jung, Kumar, Prashant, and Mulligan, Michael. Mon .
"Composite fermion nonlinear sigma models". United States. https://doi.org/10.1103/physrevb.104.125119. https://www.osti.gov/servlets/purl/1850797.
@article{osti_1850797,
title = {Composite fermion nonlinear sigma models},
author = {Lee, Chao-Jung and Kumar, Prashant and Mulligan, Michael},
abstractNote = {We study particle-hole symmetry at the integer quantum Hall plateau transition using composite fermion mean-field theory. Because this theory implicitly includes some electron-electron interactions, it also has applications to certain fractional quantum Hall plateau transitions. Previous work [P. Kumar et al., Phys. Rev. B 100, 235124 (2019)] using this approach showed that the diffusive quantum criticality of this transition is described by a nonlinear sigma model with topological θ = π term. This result, which holds for both the Dirac and Halperin, Lee, and Read composite fermion theories, signifies an emergent particle-hole (reflection) symmetry of the integer (fractional) quantum Hall transition. Here we consider the stability of this result to various particle-hole symmetry-violating perturbations. In the presence of quenched disorder that preserves particle-hole symmetry, we find that finite longitudinal conductivity at this transition requires the vanishing of a symmetry-violating composite fermion effective mass, which if present would generally lead to θ ≠ π and a corresponding violation of particle-hole symmetric electrical transport σxy ≠ $\frac1{2}$$\frac{e^2}{h}$ . When the disorder does not preserve particle-hole symmetry, we find that θ can vary continuously within the diffusive regime. Our results call for further study of the universality of the quantum Hall plateau transition.},
doi = {10.1103/physrevb.104.125119},
journal = {Physical Review. B},
number = 12,
volume = 104,
place = {United States},
year = {Mon Sep 13 00:00:00 EDT 2021},
month = {Mon Sep 13 00:00:00 EDT 2021}
}
Works referenced in this record:
Gauge-invariant response functions of fermions coupled to a gauge field
journal, December 1994
- Kim, Yong Baek; Furusaki, Akira; Wen, Xiao-Gang
- Physical Review B, Vol. 50, Issue 24
Path integral for gauge theories with fermions
journal, May 1980
- Fujikawa, Kazuo
- Physical Review D, Vol. 21, Issue 10
Duality near quantum Hall transitions
journal, May 1997
- Shimshoni, E.; Sondhi, S. L.; Shahar, D.
- Physical Review B, Vol. 55, Issue 20
Dirac Fermion Hierarchy of Composite Fermi Liquids
journal, June 2019
- Wang, Jie
- Physical Review Letters, Vol. 122, Issue 25
Is the Composite Fermion a Dirac Particle?
journal, September 2015
- Son, Dam Thanh
- Physical Review X, Vol. 5, Issue 3
Theory of anomalous quantum Hall effects in graphene
journal, May 2008
- Ostrovsky, P. M.; Gornyi, I. V.; Mirlin, A. D.
- Physical Review B, Vol. 77, Issue 19
Composite-fermion Hall conductance at ν=
journal, June 1997
- Kivelson, S. A.; Lee, D-H.; Krotov, Y.
- Physical Review B, Vol. 55, Issue 23
Generalized non-linear σ-models with gauge invariance
journal, April 1980
- Brézin, E.; Hikami, S.; Zinn-Justin, J.
- Nuclear Physics B, Vol. 165, Issue 3
Presence of quantum diffusion in two dimensions: Universal resistance at the superconductor-insulator transition
journal, January 1990
- Fisher, Matthew P. A.; Grinstein, G.; Girvin, S. M.
- Physical Review Letters, Vol. 64, Issue 5
Localization of charged quantum particles in a static random magnetic field
journal, June 1994
- Aronov, A. G.; Mirlin, A. D.; Wölfle, P.
- Physical Review B, Vol. 49, Issue 23
Quasi particles in the theory of the integral quantum Hall effect
journal, January 1987
- Pruisken, Adrianus M. M.
- Nuclear Physics B, Vol. 290
Continuous quantum phase transitions
journal, January 1997
- Sondhi, S. L.; Girvin, S. M.; Carini, J. P.
- Reviews of Modern Physics, Vol. 69, Issue 1
Critical exponent for the quantum Hall transition
journal, July 2009
- Slevin, Keith; Ohtsuki, Tomi
- Physical Review B, Vol. 80, Issue 4
Quantum Hall effect in a one-dimensional dynamical system
journal, September 2011
- Dahlhaus, J. P.; Edge, J. M.; Tworzydło, J.
- Physical Review B, Vol. 84, Issue 11
On localization in the theory of the quantized hall effect: A two-dimensional realization of the θ-vacuum
journal, June 1984
- Pruisken, A. M. M.
- Nuclear Physics B, Vol. 235, Issue 2
Dual Dirac Liquid on the Surface of the Electron Topological Insulator
journal, November 2015
- Wang, Chong; Senthil, T.
- Physical Review X, Vol. 5, Issue 4
Superuniversality of topological quantum phase transition and global phase diagram of dirty topological systems in three dimensions
journal, February 2017
- Goswami, Pallab; Chakravarty, Sudip
- Physical Review B, Vol. 95, Issue 7
Scaling in Plateau-to-Plateau Transition: A Direct Connection of Quantum Hall Systems with the Anderson Localization Model
journal, May 2009
- Li, Wanli; Vicente, C. L.; Xia, J. S.
- Physical Review Letters, Vol. 102, Issue 21
Low-Energy Theory of Disordered Graphene
journal, December 2006
- Altland, Alexander
- Physical Review Letters, Vol. 97, Issue 23
Short-range interactions and scaling near integer quantum Hall transitions
journal, March 2000
- Wang, Ziqiang; Fisher, Matthew P. A.; Girvin, S. M.
- Physical Review B, Vol. 61, Issue 12
Effect of localization on the hall conductivity in the two-dimensional system in strong magnetic fields
journal, June 1981
- Aoki, H.; Ando, T.
- Solid State Communications, Vol. 38, Issue 11
Crossover from the nonuniversal scaling regime to the universal scaling regime in quantum Hall plateau transitions
journal, January 2010
- Li, Wanli; Xia, J. S.; Vicente, C.
- Physical Review B, Vol. 81, Issue 3
Dilute instanton gas as the precursor to the integral quantum Hall effect
journal, August 1985
- Pruisken, A. M. M.
- Physical Review B, Vol. 32, Issue 4
Conformal invariance, multifractality, and finite-size scaling at Anderson localization transitions in two dimensions
journal, July 2010
- Obuse, H.; Subramaniam, A. R.; Furusaki, A.
- Physical Review B, Vol. 82, Issue 3
Theory of the half-filled Landau level
journal, March 1993
- Halperin, B. I.; Lee, Patrick A.; Read, Nicholas
- Physical Review B, Vol. 47, Issue 12
Topological field theory of time-reversal invariant insulators
journal, November 2008
- Qi, Xiao-Liang; Hughes, Taylor L.; Zhang, Shou-Cheng
- Physical Review B, Vol. 78, Issue 19, Article No. 195424
The integer quantum Hall plateau transition is a current algebra after all
journal, April 2019
- Zirnbauer, Martin R.
- Nuclear Physics B, Vol. 941
Fractional quantum Hall effect and Chern-Simons gauge theories
journal, September 1991
- Lopez, Ana; Fradkin, Eduardo
- Physical Review B, Vol. 44, Issue 10
Chiral symmetry and functional integral
journal, October 1984
- Gamboa Saravi, R. E.; Muschietti, M. A.; Schaposnik, F. A.
- Annals of Physics, Vol. 157, Issue 2
Gaussian free fields at the integer quantum Hall plateau transition
journal, May 2017
- Bondesan, R.; Wieczorek, D.; Zirnbauer, M. R.
- Nuclear Physics B, Vol. 918
Particle-Hole Symmetry and the Fractional Quantum Hall Effect in the Lowest Landau Level
journal, April 2020
- Pan, W.; Kang, W.; Lilly, M. P.
- Physical Review Letters, Vol. 124, Issue 15
Self-duality of the integer quantum Hall to insulator transition: Composite fermion description
journal, December 2019
- Kumar, Prashant; Kim, Yong Baek; Raghu, S.
- Physical Review B, Vol. 100, Issue 23
Topological quantum number and critical exponent from conductance fluctuations at the quantum Hall plateau transition
journal, December 2011
- Fulga, I. C.; Hassler, F.; Akhmerov, A. R.
- Physical Review B, Vol. 84, Issue 24
Topological phase transition underpinning particle-hole symmetry in the Halperin-Lee-Read theory
journal, September 2018
- Kumar, Prashant; Mulligan, Michael; Raghu, S.
- Physical Review B, Vol. 98, Issue 11
Effect of spin on electron motion in a random magnetic field
journal, October 2002
- Takahashi, K.; Efetov, K. B.
- Physical Review B, Vol. 66, Issue 16
Universal Conductivity at the Quantum Hall Liquid to Insulator Transition
journal, May 1995
- Shahar, D.; Tsui, D. C.; Shayegan, M.
- Physical Review Letters, Vol. 74, Issue 22
Numerical Study of the Localization Length Critical Index in a Network Model of Plateau-Plateau Transitions in the Quantum Hall Effect
journal, August 2011
- Amado, M.; Malyshev, A. V.; Sedrakyan, A.
- Physical Review Letters, Vol. 107, Issue 6
Evidence for Charge-Flux Duality near the Quantum Hall Liquid-to-Insulator Transition
journal, October 1996
- Shahar, D.; Tsui, D. C.; Shayegan, M.
- Science, Vol. 274, Issue 5287
Electron Delocalization by a Magnetic Field in Two Dimensions
journal, November 1983
- Levine, Herbert; Libby, Stephen B.; Pruisken, Adrianus M. M.
- Physical Review Letters, Vol. 51, Issue 20
On Euclidean spinors and Wick rotations
journal, December 1996
- van Nieuwenhuizen, Peter; Waldron, Andrew
- Physics Letters B, Vol. 389, Issue 1
Finite size Scaling of the Chalker-Coddington Model
journal, January 2012
- Slevin, Keith; Ohtsuki, Tomi
- International Journal of Modern Physics: Conference Series, Vol. 11
Composite fermion Hall conductivity and the half-filled Landau level
journal, June 2019
- Kumar, Prashant; Raghu, S.; Mulligan, Michael
- Physical Review B, Vol. 99, Issue 23
Emergent reflection symmetry from nonrelativistic composite fermions
journal, May 2019
- Kumar, Prashant; Mulligan, Michael; Raghu, S.
- Physical Review B, Vol. 99, Issue 20
Particle in a random magnetic field on a plane
journal, May 1993
- Khveshchenko, D. V.; Meshkov, S. V.
- Physical Review B, Vol. 47, Issue 18
Scaling, Diffusion, and the Integer Quantized Hall Effect
journal, August 1988
- Chalker, J. T.; Daniell, G. J.
- Physical Review Letters, Vol. 61, Issue 5
Particle-vortex duality of two-dimensional Dirac fermion from electric-magnetic duality of three-dimensional topological insulators
journal, June 2016
- Metlitski, Max A.; Vishwanath, Ashvin
- Physical Review B, Vol. 93, Issue 24
Numerical Study of a Dual Representation of the Integer Quantum Hall Transition
journal, February 2021
- Huang, Kevin S.; Raghu, S.; Kumar, Prashant
- Physical Review Letters, Vol. 126, Issue 5
A duality web in dimensions and condensed matter physics
journal, November 2016
- Seiberg, Nathan; Senthil, T.; Wang, Chong
- Annals of Physics, Vol. 374
Localization-length exponent in two models of quantum Hall plateau transitions
journal, January 2019
- Zhu, Qiong; Wu, Peng; Bhatt, R. N.
- Physical Review B, Vol. 99, Issue 2
Effective-Field-Theory Model for the Fractional Quantum Hall Effect
journal, January 1989
- Zhang, S. C.; Hansson, T. H.; Kivelson, S.
- Physical Review Letters, Vol. 62, Issue 1
Dirac composite fermions and emergent reflection symmetry about even-denominator filling fractions
journal, October 2018
- Goldman, Hart; Fradkin, Eduardo
- Physical Review B, Vol. 98, Issue 16
Geometrically disordered network models, quenched quantum gravity, and critical behavior at quantum Hall plateau transitions
journal, March 2017
- Gruzberg, I. A.; Klümper, A.; Nuding, W.
- Physical Review B, Vol. 95, Issue 12
Finite-Size Effects and Irrelevant Corrections to Scaling Near the Integer Quantum Hall Transition
journal, November 2012
- Obuse, Hideaki; Gruzberg, Ilya A.; Evers, Ferdinand
- Physical Review Letters, Vol. 109, Issue 20
Scaling theory of the integer quantum Hall effect
journal, April 1995
- Huckestein, Bodo
- Reviews of Modern Physics, Vol. 67, Issue 2
Theory of quantised Hall conductivity in two dimensions
journal, August 1982
- Streda, P.
- Journal of Physics C: Solid State Physics, Vol. 15, Issue 22
Non-Abelian bosonization and modular transformation approach to superuniversality
journal, March 2019
- Hui, Aaron; Kim, Eun-Ah; Mulligan, Michael
- Physical Review B, Vol. 99, Issue 12
Quantized Hall conductivity in two dimensions
journal, May 1981
- Laughlin, R. B.
- Physical Review B, Vol. 23, Issue 10
Effects of Electron-Electron Interactions on the Integer Quantum Hall Transitions
journal, May 1996
- Lee, Dung-Hai; Wang, Ziqiang
- Physical Review Letters, Vol. 76, Issue 21
Fractional Quantum Numbers on Solitons
journal, October 1981
- Goldstone, Jeffrey; Wilczek, Frank
- Physical Review Letters, Vol. 47, Issue 14
Particle-Vortex Duality from 3D Bosonization
journal, September 2016
- Karch, Andreas; Tong, David
- Physical Review X, Vol. 6, Issue 3
Composite-fermion approach for the fractional quantum Hall effect
journal, July 1989
- Jain, J. K.
- Physical Review Letters, Vol. 63, Issue 2
Particle-hole symmetry in the anomalous quantum Hall effect
journal, May 1984
- Girvin, S. M.
- Physical Review B, Vol. 29, Issue 10
Electron fractionalization for two-dimensional Dirac fermions
journal, June 2008
- Chamon, Claudio; Hou, Chang-Yu; Jackiw, Roman
- Physical Review B, Vol. 77, Issue 23
Criticality of Two-Dimensional Disordered Dirac Fermions in the Unitary Class and Universality of the Integer Quantum Hall Transition
journal, February 2021
- Sbierski, Björn; Dresselhaus, Elizabeth J.; Moore, Joel E.
- Physical Review Letters, Vol. 126, Issue 7
Particle-Hole Symmetry in the Fermion-Chern-Simons and Dirac Descriptions of a Half-Filled Landau Level
journal, August 2017
- Wang, Chong; Cooper, Nigel R.; Halperin, Bertrand I.
- Physical Review X, Vol. 7, Issue 3
Theories of low-energy quasi-particle states in disordered d-wave superconductors
journal, March 2002
- Altland, Alexander; Simons, B. D.; Zirnbauer, M. R.
- Physics Reports, Vol. 359, Issue 4
Motion of fast particles in strongly fluctuating magnetic fields
journal, November 1992
- Altshuler, B. L.; Ioffe, L. B.
- Physical Review Letters, Vol. 69, Issue 20
Quantum Criticality and Minimal Conductivity in Graphene with Long-Range Disorder
journal, June 2007
- Ostrovsky, P. M.; Gornyi, I. V.; Mirlin, A. D.
- Physical Review Letters, Vol. 98, Issue 25