NonAbelian fermionization and fractional quantum Hall transitions
There has been a recent surge of interest in dualities relating theories of ChernSimons gauge fields coupled to either bosons or fermions within the condensed matter community, particularly in the context of topological insulators and the halffilled Landau level. Here, we study the application of one such duality to the longstanding 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 ChernSimons gauge fields coupled to either bosons or fermions within the condensed matter community, particularly in the context of topological insulators and the halffilled Landau level. Here, we study the application of one such duality to the longstanding problem of quantum Hall interplateaux 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 superuniversal, 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 ChernSimons 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 nontrivial 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 ChernSimons 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]}
 Cornell Univ., Ithaca, NY (United States)
 Univ. of California, Riverside, CA (United States)
 Publication Date:
 Grant/Contract Number:
 SC0010313
 Type:
 Accepted Manuscript
 Journal Name:
 Physical Review B
 Additional Journal Information:
 Journal Volume: 97; Journal Issue: 8; Journal ID: ISSN 24699950
 Publisher:
 American Physical Society (APS)
 Research Org:
 Cornell Univ., Ithaca, NY (United States)
 Sponsoring Org:
 USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC22)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY
 OSTI Identifier:
 1423635
 Alternate Identifier(s):
 OSTI ID: 1419905
Hui, Aaron, Mulligan, Michael, and Kim, EunAh. NonAbelian fermionization and fractional quantum Hall transitions. United States: N. p.,
Web. doi:10.1103/PhysRevB.97.085112.
Hui, Aaron, Mulligan, Michael, & Kim, EunAh. NonAbelian fermionization and fractional quantum Hall transitions. United States. doi:10.1103/PhysRevB.97.085112.
Hui, Aaron, Mulligan, Michael, and Kim, EunAh. 2018.
"NonAbelian fermionization and fractional quantum Hall transitions". United States.
doi:10.1103/PhysRevB.97.085112.
@article{osti_1423635,
title = {NonAbelian fermionization and fractional quantum Hall transitions},
author = {Hui, Aaron and Mulligan, Michael and Kim, EunAh},
abstractNote = {There has been a recent surge of interest in dualities relating theories of ChernSimons gauge fields coupled to either bosons or fermions within the condensed matter community, particularly in the context of topological insulators and the halffilled Landau level. Here, we study the application of one such duality to the longstanding 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 ChernSimons gauge fields coupled to either bosons or fermions within the condensed matter community, particularly in the context of topological insulators and the halffilled Landau level. Here, we study the application of one such duality to the longstanding problem of quantum Hall interplateaux 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 superuniversal, 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 ChernSimons 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 nontrivial 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 ChernSimons 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}
}