Non-Abelian fermionization and fractional quantum Hall transitions

Journal Article · 07 February 2018 · Physical Review B

DOI: https://doi.org/10.1103/PhysRevB.97.085112 · OSTI ID:1423635

Hui, Aaron ^[1]; Mulligan, Michael ^[2]; Kim, Eun-Ah ^[3]

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1. Cornell Univ., Ithaca, NY (United States); Cornell University
2. Univ. of California, Riverside, CA (United States)
3. Cornell Univ., Ithaca, NY (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); USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22)
• Grant/Contract Number: SC0010313
• OSTI ID: 1423635
• Journal Information: Physical Review B, Journal Name: Physical Review B Journal Issue: 8 Vol. 97; ISSN 2469-9950; ISSN PRBMDO
• Publisher: American Physical Society (APS)Copyright Statement
• Country of Publication: United States
• Language: English