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Title: 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:
 [1];  [2];  [1]
  1. Cornell Univ., Ithaca, NY (United States)
  2. 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:
Journal Article: 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. doi:10.1103/PhysRevB.97.085112.
Hui, Aaron, Mulligan, Michael, and Kim, Eun-Ah. Thu . "Non-Abelian fermionization and fractional quantum Hall transitions". United States. doi: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},
issn = {2469-9950},
number = 8,
volume = 97,
place = {United States},
year = {2018},
month = {2}
}

Journal Article:
Free Publicly Available Full Text
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Cited by: 4 works
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Figures / Tables:

FIG. 1 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 » yellow points to “infinitely coupled” theories. Previous works have studied the large color and large flavor theories both in the fermionic and bosonic cases, labeled in orange and blue.19,20,34,55,56 The red dot corresponds to our physical theory, while our calculation in the Nf $\gg$ Nc expansion is done in the green region. All calculations give ν = 1 at leading order,19,20,34,55,56 while experiments give ν ≈ 2.3.1« less

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      Figures / Tables found in this record:

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