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Title: Non-Abelian fermionization and fractional quantum Hall transitions

Journal Article · · Physical Review B
 [1];  [2];  [1]
  1. Cornell Univ., Ithaca, NY (United States)
  2. Univ. of California, Riverside, CA (United States)

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)].

Research Organization:
Cornell Univ., Ithaca, NY (United States)
Sponsoring Organization:
USDOE Office of Science (SC), Basic Energy Sciences (BES)
Grant/Contract Number:
SC0010313
OSTI ID:
1423635
Alternate ID(s):
OSTI ID: 1419905
Journal Information:
Physical Review B, Vol. 97, Issue 8; ISSN 2469-9950
Publisher:
American Physical Society (APS)Copyright Statement
Country of Publication:
United States
Language:
English

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Cited By (3)

Duality web on a 3D Euclidean lattice and manifestation of hidden symmetries journal June 2019
Strong-weak Chern-Simons-matter dualities from a lattice construction journal August 2018
On the Higher Spin Spectrum of Chern-Simons Theory coupled to Fermions in the Large Flavour Limit text January 2017

Figures / Tables (2)