Composite fermion nonlinear sigma models

Lee, Chao-Jung; Kumar, Prashant; Mulligan, Michael

doi:10.1103/physrevb.104.125119

Title: Composite fermion nonlinear sigma models

Journal Article · Mon Sep 13 00:00:00 EDT 2021 · Physical Review. B

DOI:https://doi.org/10.1103/physrevb.104.125119· OSTI ID:1850797

^[1]; Kumar, Prashant ^[2]; Mulligan, Michael ^[3]

California Institute of Technology (CalTech), Pasadena, CA (United States)
Princeton Univ., NJ (United States)
Univ. of California, Riverside, CA (United States)

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 σ_xy ≠ $$\frac1{2}$$$$\frac{e^2}{h}$$ . 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.

View Accepted Manuscript (DOE)

Cite

Export

Save

Research Organization:: Princeton Univ., NJ (United States); Univ. of California, Riverside, CA (United States)

Sponsoring Organization:: USDOE Office of Science (SC)

Grant/Contract Number:: SC0002140; SC0020007

OSTI ID:: 1850797

Journal Information:: Physical Review. B, Vol. 104, Issue 12; ISSN 2469-9950

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

References (73)

Gauge-invariant response functions of fermions coupled to a gauge field Kim, Yong Baek; Furusaki, Akira; Wen, Xiao-Gang Physical Review B, Vol. 50, Issue 24 https://doi.org/10.1103/PhysRevB.50.17917	journal	December 1994
Path integral for gauge theories with fermions Fujikawa, Kazuo Physical Review D, Vol. 21, Issue 10 https://doi.org/10.1103/PhysRevD.21.2848	journal	May 1980
Duality near quantum Hall transitions Shimshoni, E.; Sondhi, S. L.; Shahar, D. Physical Review B, Vol. 55, Issue 20 https://doi.org/10.1103/PhysRevB.55.13730	journal	May 1997
Dirac Fermion Hierarchy of Composite Fermi Liquids Wang, Jie Physical Review Letters, Vol. 122, Issue 25 https://doi.org/10.1103/PhysRevLett.122.257203	journal	June 2019
Field Theories of Condensed Matter Physics Fradkin, Eduardo Cambridge University Press https://doi.org/10.1017/CBO9781139015509	book	January 2013
Is the Composite Fermion a Dirac Particle? Son, Dam Thanh Physical Review X, Vol. 5, Issue 3 https://doi.org/10.1103/PhysRevX.5.031027	journal	September 2015
Theory of anomalous quantum Hall effects in graphene Ostrovsky, P. M.; Gornyi, I. V.; Mirlin, A. D. Physical Review B, Vol. 77, Issue 19 https://doi.org/10.1103/PhysRevB.77.195430	journal	May 2008
Composite-fermion Hall conductance at ν= Kivelson, S. A.; Lee, D-H.; Krotov, Y. Physical Review B, Vol. 55, Issue 23 https://doi.org/10.1103/PhysRevB.55.15552	journal	June 1997
Generalized non-linear σ-models with gauge invariance Brézin, E.; Hikami, S.; Zinn-Justin, J. Nuclear Physics B, Vol. 165, Issue 3 https://doi.org/10.1016/0550-3213(80)90047-4	journal	April 1980
Quantum Criticality and Minimal Conductivity in Graphene with Long-Range Disorder Ostrovsky, P. M.; Gornyi, I. V.; Mirlin, A. D. Physical Review Letters, Vol. 98, Issue 25 https://doi.org/10.1103/PhysRevLett.98.256801	journal	June 2007
Presence of quantum diffusion in two dimensions: Universal resistance at the superconductor-insulator transition Fisher, Matthew P. A.; Grinstein, G.; Girvin, S. M. Physical Review Letters, Vol. 64, Issue 5 https://doi.org/10.1103/PhysRevLett.64.587	journal	January 1990
Localization of charged quantum particles in a static random magnetic field Aronov, A. G.; Mirlin, A. D.; Wölfle, P. Physical Review B, Vol. 49, Issue 23 https://doi.org/10.1103/PhysRevB.49.16609	journal	June 1994
Quasi particles in the theory of the integral quantum Hall effect Pruisken, Adrianus M. M. Nuclear Physics B, Vol. 290 https://doi.org/10.1016/0550-3213(87)90178-7	journal	January 1987
Motion of fast particles in strongly fluctuating magnetic fields Altshuler, B. L.; Ioffe, L. B. Physical Review Letters, Vol. 69, Issue 20 https://doi.org/10.1103/PhysRevLett.69.2979	journal	November 1992
Continuous quantum phase transitions Sondhi, S. L.; Girvin, S. M.; Carini, J. P. Reviews of Modern Physics, Vol. 69, Issue 1 https://doi.org/10.1103/RevModPhys.69.315	journal	January 1997
Critical exponent for the quantum Hall transition Slevin, Keith; Ohtsuki, Tomi Physical Review B, Vol. 80, Issue 4 https://doi.org/10.1103/PhysRevB.80.041304	journal	July 2009
Quantum Hall effect in a one-dimensional dynamical system Dahlhaus, J. P.; Edge, J. M.; Tworzydło, J. Physical Review B, Vol. 84, Issue 11 https://doi.org/10.1103/PhysRevB.84.115133	journal	September 2011
On localization in the theory of the quantized hall effect: A two-dimensional realization of the θ-vacuum Pruisken, A. M. M. Nuclear Physics B, Vol. 235, Issue 2 https://doi.org/10.1016/0550-3213(84)90101-9	journal	June 1984
Dual Dirac Liquid on the Surface of the Electron Topological Insulator Wang, Chong; Senthil, T. Physical Review X, Vol. 5, Issue 4 https://doi.org/10.1103/PhysRevX.5.041031	journal	November 2015
Superuniversality of topological quantum phase transition and global phase diagram of dirty topological systems in three dimensions Goswami, Pallab; Chakravarty, Sudip Physical Review B, Vol. 95, Issue 7 https://doi.org/10.1103/PhysRevB.95.075131	journal	February 2017
Scaling in Plateau-to-Plateau Transition: A Direct Connection of Quantum Hall Systems with the Anderson Localization Model Li, Wanli; Vicente, C. L.; Xia, J. S. Physical Review Letters, Vol. 102, Issue 21 https://doi.org/10.1103/PhysRevLett.102.216801	journal	May 2009
Universal conductance in the lowest Landau level Huo, Y.; Hetzel, R. E.; Bhatt, R. N. Physical Review Letters, Vol. 70, Issue 4 https://doi.org/10.1103/PhysRevLett.70.481	journal	January 1993
Low-Energy Theory of Disordered Graphene Altland, Alexander Physical Review Letters, Vol. 97, Issue 23 https://doi.org/10.1103/PhysRevLett.97.236802	journal	December 2006
Short-range interactions and scaling near integer quantum Hall transitions Wang, Ziqiang; Fisher, Matthew P. A.; Girvin, S. M. Physical Review B, Vol. 61, Issue 12 https://doi.org/10.1103/PhysRevB.61.8326	journal	March 2000
Effect of localization on the hall conductivity in the two-dimensional system in strong magnetic fields Aoki, H.; Ando, T. Solid State Communications, Vol. 38, Issue 11 https://doi.org/10.1016/0038-1098(81)90021-1	journal	June 1981
Crossover from the nonuniversal scaling regime to the universal scaling regime in quantum Hall plateau transitions Li, Wanli; Xia, J. S.; Vicente, C. Physical Review B, Vol. 81, Issue 3 https://doi.org/10.1103/PhysRevB.81.033305	journal	January 2010
Dilute instanton gas as the precursor to the integral quantum Hall effect Pruisken, A. M. M. Physical Review B, Vol. 32, Issue 4 https://doi.org/10.1103/PhysRevB.32.2636	journal	August 1985
Conformal invariance, multifractality, and finite-size scaling at Anderson localization transitions in two dimensions Obuse, H.; Subramaniam, A. R.; Furusaki, A. Physical Review B, Vol. 82, Issue 3 https://doi.org/10.1103/PhysRevB.82.035309	journal	July 2010
Theory of the half-filled Landau level Halperin, B. I.; Lee, Patrick A.; Read, Nicholas Physical Review B, Vol. 47, Issue 12 https://doi.org/10.1103/PhysRevB.47.7312	journal	March 1993
Topological field theory of time-reversal invariant insulators Qi, Xiao-Liang; Hughes, Taylor L.; Zhang, Shou-Cheng Physical Review B, Vol. 78, Issue 19, Article No. 195424 https://doi.org/10.1103/PhysRevB.78.195424	journal	November 2008
The integer quantum Hall plateau transition is a current algebra after all Zirnbauer, Martin R. Nuclear Physics B, Vol. 941 https://doi.org/10.1016/j.nuclphysb.2019.02.017	journal	April 2019
Fractional quantum Hall effect and Chern-Simons gauge theories Lopez, Ana; Fradkin, Eduardo Physical Review B, Vol. 44, Issue 10 https://doi.org/10.1103/PhysRevB.44.5246	journal	September 1991
Chiral symmetry and functional integral Gamboa Saravi, R. E.; Muschietti, M. A.; Schaposnik, F. A. Annals of Physics, Vol. 157, Issue 2 https://doi.org/10.1016/0003-4916(84)90065-4	journal	October 1984
Gaussian free fields at the integer quantum Hall plateau transition Bondesan, R.; Wieczorek, D.; Zirnbauer, M. R. Nuclear Physics B, Vol. 918 https://doi.org/10.1016/j.nuclphysb.2017.02.011	journal	May 2017
Particle-Hole Symmetry and the Fractional Quantum Hall Effect in the Lowest Landau Level Pan, W.; Kang, W.; Lilly, M. P. Physical Review Letters, Vol. 124, Issue 15 https://doi.org/10.1103/PhysRevLett.124.156801	journal	April 2020
Self-duality of the integer quantum Hall to insulator transition: Composite fermion description Kumar, Prashant; Kim, Yong Baek; Raghu, S. Physical Review B, Vol. 100, Issue 23 https://doi.org/10.1103/PhysRevB.100.235124	journal	December 2019
Topological quantum number and critical exponent from conductance fluctuations at the quantum Hall plateau transition Fulga, I. C.; Hassler, F.; Akhmerov, A. R. Physical Review B, Vol. 84, Issue 24 https://doi.org/10.1103/PhysRevB.84.245447	journal	December 2011
Topological phase transition underpinning particle-hole symmetry in the Halperin-Lee-Read theory Kumar, Prashant; Mulligan, Michael; Raghu, S. Physical Review B, Vol. 98, Issue 11 https://doi.org/10.1103/PhysRevB.98.115105	journal	September 2018
Effect of spin on electron motion in a random magnetic field Takahashi, K.; Efetov, K. B. Physical Review B, Vol. 66, Issue 16 https://doi.org/10.1103/PhysRevB.66.165304	journal	October 2002
Universal Conductivity at the Quantum Hall Liquid to Insulator Transition Shahar, D.; Tsui, D. C.; Shayegan, M. Physical Review Letters, Vol. 74, Issue 22 https://doi.org/10.1103/PhysRevLett.74.4511	journal	May 1995
Numerical Study of the Localization Length Critical Index in a Network Model of Plateau-Plateau Transitions in the Quantum Hall Effect Amado, M.; Malyshev, A. V.; Sedrakyan, A. Physical Review Letters, Vol. 107, Issue 6 https://doi.org/10.1103/PhysRevLett.107.066402	journal	August 2011
Evidence for Charge-Flux Duality near the Quantum Hall Liquid-to-Insulator Transition Shahar, D.; Tsui, D. C.; Shayegan, M. Science, Vol. 274, Issue 5287 https://doi.org/10.1126/science.274.5287.589	journal	October 1996
Electron Delocalization by a Magnetic Field in Two Dimensions Levine, Herbert; Libby, Stephen B.; Pruisken, Adrianus M. M. Physical Review Letters, Vol. 51, Issue 20 https://doi.org/10.1103/PhysRevLett.51.1915	journal	November 1983
On Euclidean spinors and Wick rotations van Nieuwenhuizen, Peter; Waldron, Andrew Physics Letters B, Vol. 389, Issue 1 https://doi.org/10.1016/S0370-2693(96)01251-8	journal	December 1996
Condensed Matter Field Theory Altland, Alexander; Simons, Ben D. https://doi.org/10.1017/CBO9780511789984	book	August 2010
Finite size Scaling of the Chalker-Coddington Model Slevin, Keith; Ohtsuki, Tomi International Journal of Modern Physics: Conference Series, Vol. 11 https://doi.org/10.1142/S2010194512006162	journal	January 2012
Composite fermion Hall conductivity and the half-filled Landau level Kumar, Prashant; Raghu, S.; Mulligan, Michael Physical Review B, Vol. 99, Issue 23 https://doi.org/10.1103/PhysRevB.99.235114	journal	June 2019
Emergent reflection symmetry from nonrelativistic composite fermions Kumar, Prashant; Mulligan, Michael; Raghu, S. Physical Review B, Vol. 99, Issue 20 https://doi.org/10.1103/PhysRevB.99.205151	journal	May 2019
Particle in a random magnetic field on a plane Khveshchenko, D. V.; Meshkov, S. V. Physical Review B, Vol. 47, Issue 18 https://doi.org/10.1103/PhysRevB.47.12051	journal	May 1993
Scaling, Diffusion, and the Integer Quantized Hall Effect Chalker, J. T.; Daniell, G. J. Physical Review Letters, Vol. 61, Issue 5 https://doi.org/10.1103/PhysRevLett.61.593	journal	August 1988
Particle-vortex duality of two-dimensional Dirac fermion from electric-magnetic duality of three-dimensional topological insulators Metlitski, Max A.; Vishwanath, Ashvin Physical Review B, Vol. 93, Issue 24 https://doi.org/10.1103/PhysRevB.93.245151	journal	June 2016
Numerical Study of a Dual Representation of the Integer Quantum Hall Transition Huang, Kevin S.; Raghu, S.; Kumar, Prashant Physical Review Letters, Vol. 126, Issue 5 https://doi.org/10.1103/PhysRevLett.126.056802	journal	February 2021
Composite Fermions Jain, Jainendra K. https://doi.org/10.1017/CBO9780511607561	book	January 2007
A duality web in $2 + 1$ dimensions and condensed matter physics Seiberg, Nathan; Senthil, T.; Wang, Chong Annals of Physics, Vol. 374 https://doi.org/10.1016/j.aop.2016.08.007	journal	November 2016
Localization-length exponent in two models of quantum Hall plateau transitions Zhu, Qiong; Wu, Peng; Bhatt, R. N. Physical Review B, Vol. 99, Issue 2 https://doi.org/10.1103/PhysRevB.99.024205	journal	January 2019
Effective-Field-Theory Model for the Fractional Quantum Hall Effect Zhang, S. C.; Hansson, T. H.; Kivelson, S. Physical Review Letters, Vol. 62, Issue 1 https://doi.org/10.1103/PhysRevLett.62.82	journal	January 1989
Dirac composite fermions and emergent reflection symmetry about even-denominator filling fractions Goldman, Hart; Fradkin, Eduardo Physical Review B, Vol. 98, Issue 16 https://doi.org/10.1103/PhysRevB.98.165137	journal	October 2018
Geometrically disordered network models, quenched quantum gravity, and critical behavior at quantum Hall plateau transitions Gruzberg, I. A.; Klümper, A.; Nuding, W. Physical Review B, Vol. 95, Issue 12 https://doi.org/10.1103/PhysRevB.95.125414	journal	March 2017
Finite-Size Effects and Irrelevant Corrections to Scaling Near the Integer Quantum Hall Transition Obuse, Hideaki; Gruzberg, Ilya A.; Evers, Ferdinand Physical Review Letters, Vol. 109, Issue 20 https://doi.org/10.1103/PhysRevLett.109.206804	journal	November 2012
Scaling theory of the integer quantum Hall effect Huckestein, Bodo Reviews of Modern Physics, Vol. 67, Issue 2 https://doi.org/10.1103/RevModPhys.67.357	journal	April 1995
Theory of quantised Hall conductivity in two dimensions Streda, P. Journal of Physics C: Solid State Physics, Vol. 15, Issue 22 https://doi.org/10.1088/0022-3719/15/22/005	journal	August 1982
Non-Abelian bosonization and modular transformation approach to superuniversality Hui, Aaron; Kim, Eun-Ah; Mulligan, Michael Physical Review B, Vol. 99, Issue 12 https://doi.org/10.1103/PhysRevB.99.125135	journal	March 2019
Quantized Hall conductivity in two dimensions Laughlin, R. B. Physical Review B, Vol. 23, Issue 10 https://doi.org/10.1103/PhysRevB.23.5632	journal	May 1981
Effects of Electron-Electron Interactions on the Integer Quantum Hall Transitions Lee, Dung-Hai; Wang, Ziqiang Physical Review Letters, Vol. 76, Issue 21 https://doi.org/10.1103/PhysRevLett.76.4014	journal	May 1996
Fractional Quantum Numbers on Solitons Goldstone, Jeffrey; Wilczek, Frank Physical Review Letters, Vol. 47, Issue 14 https://doi.org/10.1103/PhysRevLett.47.986	journal	October 1981
Particle-Vortex Duality from 3D Bosonization Karch, Andreas; Tong, David Physical Review X, Vol. 6, Issue 3 https://doi.org/10.1103/PhysRevX.6.031043	journal	September 2016
Composite-fermion approach for the fractional quantum Hall effect Jain, J. K. Physical Review Letters, Vol. 63, Issue 2 https://doi.org/10.1103/PhysRevLett.63.199	journal	July 1989
Particle-hole symmetry in the anomalous quantum Hall effect Girvin, S. M. Physical Review B, Vol. 29, Issue 10 https://doi.org/10.1103/PhysRevB.29.6012	journal	May 1984
Electron fractionalization for two-dimensional Dirac fermions Chamon, Claudio; Hou, Chang-Yu; Jackiw, Roman Physical Review B, Vol. 77, Issue 23 https://doi.org/10.1103/PhysRevB.77.235431	journal	June 2008
Criticality of Two-Dimensional Disordered Dirac Fermions in the Unitary Class and Universality of the Integer Quantum Hall Transition Sbierski, Björn; Dresselhaus, Elizabeth J.; Moore, Joel E. Physical Review Letters, Vol. 126, Issue 7 https://doi.org/10.1103/PhysRevLett.126.076801	journal	February 2021
Particle-Hole Symmetry in the Fermion-Chern-Simons and Dirac Descriptions of a Half-Filled Landau Level Wang, Chong; Cooper, Nigel R.; Halperin, Bertrand I. Physical Review X, Vol. 7, Issue 3 https://doi.org/10.1103/PhysRevX.7.031029	journal	August 2017
Theories of low-energy quasi-particle states in disordered d-wave superconductors Altland, Alexander; Simons, B. D.; Zirnbauer, M. R. Physics Reports, Vol. 359, Issue 4 https://doi.org/10.1016/s0370-1573(01)00065-5	journal	March 2002
Scaling Theory of the Integer Quantum Hall Effect Huckestein, Bodo arXiv https://doi.org/10.48550/arxiv.cond-mat/9501106	text	January 1995

Similar Records

Composite fermion Hall conductivity and the half-filled Landau level

Journal Article · Fri Jun 07 00:00:00 EDT 2019 · Physical Review. B · OSTI ID:1850797

Kumar, Prashant; Raghu, S.; Mulligan, Michael

Topological phase transition underpinning particle-hole symmetry in the Halperin-Lee-Read theory

Journal Article · Wed Sep 05 00:00:00 EDT 2018 · Physical Review. B · OSTI ID:1850797

Kumar, Prashant; Mulligan, Michael; Raghu, S.

Particle-hole symmetry and electromagnetic response of a half-filled Landau level

Journal Article · Wed Mar 15 00:00:00 EDT 2017 · Physical Review B · OSTI ID:1850797

Levin, Michael; Son, Dam Thanh

Related Subjects

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

Title: Composite fermion nonlinear sigma models

Citation Formats

References (73)

Similar Records

Related Subjects