TY - JOUR
T1 - Non-Abelian fermionization and fractional quantum Hall transitions
AU - Hui, Aaron
AU - Mulligan, Michael
AU - Kim, Eun Ah
N1 - Funding Information:
We would like to thank S. Chakravarty, G.Y. Cho, M. Fisher, T. Hartman, S. Jain, S. Kivelson, M. Lawler, S. Prakash, S. Sachdev, E. Shimshoni, and S. Sondhi for helpful discussions and comments. A.H. was supported by the National Science Foundation Graduate Research Fellowship under Grant No. DGE-1650441. M.M. was supported in part by the UCR Academic Senate. M.M. is grateful for the generous hospitality of the Aspen Center for Physics, which is supported by the National Science Foundation (NSF) grant PHY-1607611. E.-A.K. was supported by the US Department of Energy, Office of Basic Energy Sciences, Division of Materials Science and Engineering under Award DE-SC0010313. E.-A.K. acknowledges Simons Fellow in Theoretical Physics Award No. 392182. The authors are also grateful for the hospitality of the Kavli Institute for Theoretical Physics, under Grant No. NSF PHY-1125915, where some of this work was performed.
Funding Information:
A.H. was supported by the National Science Foundation Graduate Research Fellowship under Grant No. DGE-1650441. M.M. was supported in part by the UCR Academic Senate. M.M. is grateful for the generous hospitality of the Aspen Center for Physics, which is supported by the National Science Foundation (NSF) grant PHY-1607611. E.-A.K. was supported by the US Department of Energy, Office of Basic Energy Sciences, Division of Materials Science and Engineering under Award DE-SC0010313. E.-A.K. acknowledges Simons Fellow in Theoretical Physics Award No. 392182. The authors are also grateful for the hospitality of the Kavli Institute for Theoretical Physics, under Grant No. NSF PHY-1125915, where some of this work was performed.
Publisher Copyright:
© 2018 American Physical Society.
PY - 2018/2/8
Y1 - 2018/2/8
N2 - 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 exponent ν≈2.3 and that ν is observed to be superuniversal, i.e., the same in the vicinity of distinct critical points [Sondhi, Rev. Mod. Phys. 69, 315 (1997)RMPHAT0034-686110.1103/RevModPhys.69.315]. Duality motivates effective descriptions for a fractional quantum Hall plateau transition involving a Chern-Simons field with U(Nc) gauge group coupled to Nf=1 fermion. We study one class of theories in a controlled limit where Nf Nc and calculate ν to leading nontrivial order in the absence of disorder. Although these theories do not yield an anomalously large exponent ν within the large Nf Nc expansion, they do offer a new parameter space of theories that is apparently different from prior works involving Abelian Chern-Simons gauge fields [Wen and Wu, Phys. Rev. Lett. 70, 1501 (1993)PRLTAO0031-900710.1103/PhysRevLett.70.1501; Chen, Phys. Rev. B 48, 13749 (1993)PRBMDO0163-182910.1103/PhysRevB.48.13749].
AB - 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 exponent ν≈2.3 and that ν is observed to be superuniversal, i.e., the same in the vicinity of distinct critical points [Sondhi, Rev. Mod. Phys. 69, 315 (1997)RMPHAT0034-686110.1103/RevModPhys.69.315]. Duality motivates effective descriptions for a fractional quantum Hall plateau transition involving a Chern-Simons field with U(Nc) gauge group coupled to Nf=1 fermion. We study one class of theories in a controlled limit where Nf Nc and calculate ν to leading nontrivial order in the absence of disorder. Although these theories do not yield an anomalously large exponent ν within the large Nf Nc expansion, they do offer a new parameter space of theories that is apparently different from prior works involving Abelian Chern-Simons gauge fields [Wen and Wu, Phys. Rev. Lett. 70, 1501 (1993)PRLTAO0031-900710.1103/PhysRevLett.70.1501; Chen, Phys. Rev. B 48, 13749 (1993)PRBMDO0163-182910.1103/PhysRevB.48.13749].
UR - http://www.scopus.com/inward/record.url?scp=85042173956&partnerID=8YFLogxK
U2 - 10.1103/PhysRevB.97.085112
DO - 10.1103/PhysRevB.97.085112
M3 - Article
AN - SCOPUS:85042173956
SN - 2469-9950
VL - 97
JO - Physical Review B
JF - Physical Review B
IS - 8
M1 - 085112
ER -