Non-Abelian fermionization and fractional quantum Hall transitions
Abstract
There has been a recent surge of interest in dualities relating theories of Chern-Simons gauge fields coupled to either bosons or fermions within the condensed matter community, particularly in the context of topological insulators and the half-filled Landau level. Here, we study the application of one such duality to the long-standing problem of quantum Hall interplateaux transitions. The key motivating experimental observations are the anomalously large value of the correlation length There has been a recent surge of interest in dualities relating theories of Chern-Simons gauge fields coupled to either bosons or fermions within the condensed matter community, particularly in the context of topological insulators and the half-filled Landau level. Here, we study the application of one such duality to the long-standing problem of quantum Hall inter-plateaux transitions. The key motivating experimental observations are the anomalously large value of the correlation length exponent $$\nu \approx 2.3$$ and that $$\nu$$ is observed to be super-universal, i.e., the same in the vicinity of distinct critical points [S.L. Sondhi et al., Rev. Mod. Phys. \textbf{69}, 315 (1997)]. Duality motivates effective descriptions for a fractional quantum Hall plateau transition involving a Chern-Simons field with $$U(N_c)$$ gauge group coupled to $$N_f = 1$$ fermion. We study one class of theories in a controlled limit where $$N_f \gg N_c$$ and calculate $$\nu$$ to leading non-trivial order in the absence of disorder. Although these theories do not yield an anomalously large exponent $$\nu$$ within the large $$N_f \gg N_c$$ expansion, they do offer a new parameter space of theories that is apparently different from prior works involving abelian Chern-Simons gauge fields [X.-G. Wen and Y.-S. Wu, Phys. Rev. Lett. \textbf{70}, 1501 (1993); W. Chen. et al., Phys. Rev. B. \textbf{48}, 13749 (1993)].
- Authors:
-
- Cornell Univ., Ithaca, NY (United States)
- Univ. of California, Riverside, CA (United States)
- Publication Date:
- Research Org.:
- Cornell Univ., Ithaca, NY (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC), Basic Energy Sciences (BES)
- OSTI Identifier:
- 1423635
- Alternate Identifier(s):
- OSTI ID: 1419905
- Grant/Contract Number:
- SC0010313
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Physical Review B
- Additional Journal Information:
- Journal Volume: 97; Journal Issue: 8; 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
Citation Formats
Hui, Aaron, Mulligan, Michael, and Kim, Eun-Ah. Non-Abelian fermionization and fractional quantum Hall transitions. United States: N. p., 2018.
Web. doi:10.1103/PhysRevB.97.085112.
Hui, Aaron, Mulligan, Michael, & Kim, Eun-Ah. Non-Abelian fermionization and fractional quantum Hall transitions. United States. https://doi.org/10.1103/PhysRevB.97.085112
Hui, Aaron, Mulligan, Michael, and Kim, Eun-Ah. Thu .
"Non-Abelian fermionization and fractional quantum Hall transitions". United States. https://doi.org/10.1103/PhysRevB.97.085112. https://www.osti.gov/servlets/purl/1423635.
@article{osti_1423635,
title = {Non-Abelian fermionization and fractional quantum Hall transitions},
author = {Hui, Aaron and Mulligan, Michael and Kim, Eun-Ah},
abstractNote = {There has been a recent surge of interest in dualities relating theories of Chern-Simons gauge fields coupled to either bosons or fermions within the condensed matter community, particularly in the context of topological insulators and the half-filled Landau level. Here, we study the application of one such duality to the long-standing problem of quantum Hall interplateaux transitions. The key motivating experimental observations are the anomalously large value of the correlation length There has been a recent surge of interest in dualities relating theories of Chern-Simons gauge fields coupled to either bosons or fermions within the condensed matter community, particularly in the context of topological insulators and the half-filled Landau level. Here, we study the application of one such duality to the long-standing problem of quantum Hall inter-plateaux transitions. The key motivating experimental observations are the anomalously large value of the correlation length exponent $\nu \approx 2.3$ and that $\nu$ is observed to be super-universal, i.e., the same in the vicinity of distinct critical points [S.L. Sondhi et al., Rev. Mod. Phys. \textbf{69}, 315 (1997)]. Duality motivates effective descriptions for a fractional quantum Hall plateau transition involving a Chern-Simons field with $U(N_c)$ gauge group coupled to $N_f = 1$ fermion. We study one class of theories in a controlled limit where $N_f \gg N_c$ and calculate $\nu$ to leading non-trivial order in the absence of disorder. Although these theories do not yield an anomalously large exponent $\nu$ within the large $N_f \gg N_c$ expansion, they do offer a new parameter space of theories that is apparently different from prior works involving abelian Chern-Simons gauge fields [X.-G. Wen and Y.-S. Wu, Phys. Rev. Lett. \textbf{70}, 1501 (1993); W. Chen. et al., Phys. Rev. B. \textbf{48}, 13749 (1993)].},
doi = {10.1103/PhysRevB.97.085112},
journal = {Physical Review B},
number = 8,
volume = 97,
place = {United States},
year = {2018},
month = {2}
}
Free Publicly Available Full Text
Publisher's Version of Record
Other availability
Search WorldCat to find libraries that may hold this journal
Cited by: 4 works
Citation information provided by
Web of Science
Web of Science
Figures / Tables:
FIG. 1: A schematic plot of parameter space for ChernSimons theories with bosonic and fermionic matter. Note that the orientation of the y-axis is inverted between the bosonic and fermionic cubes. The double arrows indicate a duality between the connected points. The pink points refer to free theories and themore »
All figures and tables
(2 total)
Save to My Library
You must Sign In or Create an Account in order to save documents to your library.
Works referenced in this record:
Duality near quantum Hall transitions
journal, May 1997
- Shimshoni, E.; Sondhi, S. L.; Shahar, D.
- Physical Review B, Vol. 55, Issue 20
Is the Composite Fermion a Dirac Particle?
journal, September 2015
- Son, Dam Thanh
- Physical Review X, Vol. 5, Issue 3
Current scaling in the integer quantum Hall effect
journal, November 1994
- Wei, H. P.; Engel, L. W.; Tsui, D. C.
- Physical Review B, Vol. 50, Issue 19
Duality between SU(N)k and SU(k)N WZW models
journal, December 1990
- Naculich, Stephen G.; Schnitzer, Howard J.
- Nuclear Physics B, Vol. 347, Issue 3
Baryons, monopoles and dualities in Chern-Simons-matter theories
journal, February 2016
- Aharony, Ofer
- Journal of High Energy Physics, Vol. 2016, Issue 2
Continuous quantum phase transitions
journal, January 1997
- Sondhi, S. L.; Girvin, S. M.; Carini, J. P.
- Reviews of Modern Physics, Vol. 69, Issue 1
Large scale physics of the quantum hall fluid
journal, October 1991
- Fröhlich, J.; Zee, A.
- Nuclear Physics B, Vol. 364, Issue 3
Bosonic Analogue of Dirac Composite Fermi Liquid
journal, September 2016
- Mross, David F.; Alicea, Jason; Motrunich, Olexei I.
- Physical Review Letters, Vol. 117, Issue 13
Boson localization and the superfluid-insulator transition
journal, July 1989
- Fisher, Matthew P. A.; Weichman, Peter B.; Grinstein, G.
- Physical Review B, Vol. 40, Issue 1
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
Anomalous dimensions in non-supersymmetric bifundamental Chern-Simons theories
journal, September 2014
- Gurucharan, V.; Prakash, Shiroman
- Journal of High Energy Physics, Vol. 2014, Issue 9
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
Mirror symmetry and the half-filled Landau level
journal, December 2015
- Kachru, Shamit; Mulligan, Michael; Torroba, Gonzalo
- Physical Review B, Vol. 92, Issue 23
Quantum sine-Gordon equation as the massive Thirring model
journal, April 1975
- Coleman, Sidney
- Physical Review D, Vol. 11, Issue 8
The Chern-Simons-Landau-Ginzburg Theory of the Fractional Quantum hall Effect
journal, March 1992
- Zhang, Shou Cheng
- International Journal of Modern Physics B, Vol. 06, Issue 05n06
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
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
Lectures on supersymmetric gauge theories and electric-magnetic duality
journal, February 1996
- Intriligator, K.; Seiberg, N.
- Nuclear Physics B - Proceedings Supplements, Vol. 45, Issue 2-3
Half-filled Landau level, topological insulator surfaces, and three-dimensional quantum spin liquids
journal, February 2016
- Wang, Chong; Senthil, T.
- Physical Review B, Vol. 93, Issue 8
Large N field theories, string theory and gravity
journal, January 2000
- Aharony, Ofer; Gubser, Steven S.; Maldacena, Juan
- Physics Reports, Vol. 323, Issue 3-4
The thermal free energy in large N Chern-Simons-matter theories
journal, March 2013
- Aharony, Ofer; Giombi, Simone; Gur-Ari, Guy
- Journal of High Energy Physics, Vol. 2013, Issue 3
Emergent particle-hole symmetry in the half-filled Landau level
journal, August 2016
- Mulligan, Michael; Raghu, S.; Fisher, Matthew P. A.
- Physical Review B, Vol. 94, Issue 7
Anomalous dimensions of scalar operators in QED3
journal, August 2016
- Chester, Shai M.; Pufu, Silviu S.
- Journal of High Energy Physics, Vol. 2016, Issue 8
Fractional quantum Hall effect and Chern-Simons gauge theories
journal, September 1991
- Lopez, Ana; Fradkin, Eduardo
- Physical Review B, Vol. 44, Issue 10
Chern–Simons theory with vector fermion matter
journal, August 2012
- Giombi, Simone; Minwalla, Shiraz; Prakash, Shiroman
- The European Physical Journal C, Vol. 72, Issue 8
Single-particle states, Kohn anomaly, and pairing fluctuations in one dimension
journal, April 1974
- Luther, A.; Peschel, I.
- Physical Review B, Vol. 9, Issue 7
Experiments on Delocalization and University in the Integral Quantum Hall Effect
journal, September 1988
- Wei, H. P.; Tsui, D. C.; Paalanen, M. A.
- Physical Review Letters, Vol. 61, Issue 11
Correlation functions of large N Chern-Simons-Matter theories and bosonization in three dimensions
journal, December 2012
- Aharony, Ofer; Gur-Ari, Guy; Yacoby, Ran
- Journal of High Energy Physics, Vol. 2012, Issue 12
Explicit Derivation of Duality between a Free Dirac Cone and Quantum Electrodynamics in ( ) Dimensions
journal, June 2016
- Mross, David F.; Alicea, Jason; Motrunich, Olexei I.
- Physical Review Letters, Vol. 117, Issue 1
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
Anyon Superconductivity and the Fractional Quantum-Hall Effect
journal, June 1991
- Lee, Dung-Hai
- International Journal of Modern Physics B, Vol. 05, Issue 10
Microwave frequency dependence of integer quantum Hall effect: Evidence for finite-frequency scaling
journal, October 1993
- Engel, L. W.; Shahar, D.; Kurdak, Ç.
- Physical Review Letters, Vol. 71, Issue 16
Self-dual quantum electrodynamics as boundary state of the three-dimensional bosonic topological insulator
journal, December 2015
- Xu, Cenke; You, Yi-Zhuang
- Physical Review B, Vol. 92, Issue 22
Mott transition in an anyon gas
journal, November 1993
- Chen, Wei; Fisher, Matthew P. A.; Wu, Yong-Shi
- Physical Review B, Vol. 48, Issue 18
Nonzero-temperature transport near fractional quantum Hall critical points
journal, March 1998
- Sachdev, Subir
- Physical Review B, Vol. 57, Issue 12
Soliton operators for the quantized sine-Gordon equation
journal, May 1975
- Mandelstam, S.
- Physical Review D, Vol. 11, Issue 10
Duality in field theory and statistical systems
journal, April 1980
- Savit, Robert
- Reviews of Modern Physics, Vol. 52, Issue 2
Monopoles, duality and chiral symmetry breaking in N = 2 supersymmetric QCD
journal, December 1994
- Seiberg, N.; Witten, E.
- Nuclear Physics B, Vol. 431, Issue 3
The half-filled 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
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
d = 3 bosonic vector models coupled to Chern-Simons gauge theories
journal, March 2012
- Aharony, Ofer; Gur-Ari, Guy; Yacoby, Ran
- Journal of High Energy Physics, Vol. 2012, Issue 3
On the higher-spin spectrum in large N Chern-Simons vector models
journal, January 2017
- Giombi, S.; Gurucharan, V.; Kirilin, V.
- Journal of High Energy Physics, Vol. 2017, Issue 1
A duality web in dimensions and condensed matter physics
journal, November 2016
- Seiberg, Nathan; Senthil, T.; Wang, Chong
- Annals of Physics, Vol. 374
Effective-Field-Theory Model for the Fractional Quantum Hall Effect
journal, February 1989
- Zhang, S. C.; Hansson, T. H.; Kivelson, S.
- Physical Review Letters, Vol. 62, Issue 8
Critical exponent in the fractional quantum Hall effect
journal, April 1990
- Engel, L.; Wei, H. P.; Tsui, D. C.
- Surface Science, Vol. 229, Issue 1-3
Composite fermion duality for half-filled multicomponent Landau levels
journal, February 2017
- Sodemann, Inti; Kimchi, Itamar; Wang, Chong
- Physical Review B, Vol. 95, Issue 8
Level/rank duality and Chern-Simons-matter theories
journal, September 2016
- Hsin, Po-Shen; Seiberg, Nathan
- Journal of High Energy Physics, Vol. 2016, Issue 9
Two-loop analysis of non-Abelian Chern-Simons theory
journal, December 1992
- Chen, Wei; Semenoff, Gordon W.; Wu, Yong-Shi
- Physical Review D, Vol. 46, Issue 12
Disorder-tuned transition between a quantum Hall liquid and Hall insulator
journal, June 1995
- Wong, L. W.; Jiang, H. W.; Trivedi, N.
- Physical Review B, Vol. 51, Issue 24
Phase Transition in a Lattice Model of Superconductivity
journal, November 1981
- Dasgupta, C.; Halperin, B. I.
- Physical Review Letters, Vol. 47, Issue 21
Correspondence between two-dimensional bosons and a bulk superconductor in a magnetic field
journal, February 1989
- Fisher, Matthew P. A.; Lee, D. H.
- Physical Review B, Vol. 39, Issue 4
Particle-Vortex Duality from 3D Bosonization
journal, September 2016
- Karch, Andreas; Tong, David
- Physical Review X, Vol. 6, Issue 3
Global phase diagram in the quantum Hall effect
journal, July 1992
- Kivelson, Steven; Lee, Dung-Hai; Zhang, Shou-Cheng
- Physical Review B, Vol. 46, Issue 4
Mandelstam-'t Hooft duality in abelian lattice models
journal, July 1978
- Peskin, Michael E.
- Annals of Physics, Vol. 113, Issue 1
Level-rank duality of WZW models in conformal field theory
journal, February 1992
- Nakanishi, Tomoki; Tsuchiya, Akihiro
- Communications in Mathematical Physics, Vol. 144, Issue 2
Scaling theory of the fractional quantum Hall effect
journal, March 1990
- Jain, J. K.; Kivelson, S. A.; Trivedi, Nandini
- Physical Review Letters, Vol. 64, Issue 11
Transitions between the quantum Hall states and insulators induced by periodic potentials
journal, March 1993
- Wen, Xiao-Gang; Wu, Yong-Shi
- Physical Review Letters, Vol. 70, Issue 10
Works referencing / citing this record:
On the higher spin spectrum of Chern-Simons theory coupled to fermions in the large flavour limit
journal, February 2018
- Charan, V. Guru; Prakash, Shiroman
- Journal of High Energy Physics, Vol. 2018, Issue 2
Duality web on a 3D Euclidean lattice and manifestation of hidden symmetries
journal, June 2019
- Son, Jun Ho; Chen, Jing-Yuan; Raghu, S.
- Journal of High Energy Physics, Vol. 2019, Issue 6
Strong-weak Chern-Simons-matter dualities from a lattice construction
journal, August 2018
- Chen, Jing-Yuan; Zimet, Max
- Journal of High Energy Physics, Vol. 2018, Issue 8
Emergent Multi-Flavor QED 3 at the Plateau Transition between Fractional Chern Insulators: Applications to Graphene Heterostructures
journal, July 2018
- Lee, Jong Yeon; Wang, Chong; Zaletel, Michael P.
- Physical Review X, Vol. 8, Issue 3
On the Higher Spin Spectrum of Chern-Simons Theory coupled to Fermions in the Large Flavour Limit
text, January 2017
- Charan, V. Guru; Prakash, Shiroman
- arXiv
Figures/Tables have been extracted from DOE-funded journal article accepted manuscripts.