Non-Abelian bosonization and modular transformation approach to superuniversality
Abstract
Quantum Hall inter-plateau transitions are physical exemplars of quantum phase transitions. Near each of these transitions, the measured electrical conductivity scales with the same correlation length and dynamical critical exponents, i.e., the critical points are superuniversal. In apparent contradiction to these experiments, prior theoretical studies of quantum Hall phase transitions within the framework of Abelian Chern-Simons theory coupled to matter found correlation length exponents that depend on the value of the quantum critical Hall conductivity. Here, we use non-Abelian bosonization and modular transformations to theoretically study the phenomenon of superuniversality. Specifically, we introduce a new effective theory that has an emergent U(N) gauge symmetry with any N > 1 for a quantum phase transition between an integer quantum Hall state and an insulator. We then use modular transformations to generate from this theory effective descriptions for transitions between a large class of fractional quantum Hall states whose quasiparticle excitations have Abelian statistics. We find the correlation length and dynamical critical exponents are independent of the particular transition within a controlled 't Hooft large N expansion, i.e., superuniversal! Furthermore, we argue that this superuniversality could survive away from this controlled large N limit using recent duality conjectures.
- Authors:
-
- Cornell Univ., Ithaca, NY (United States)
- 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). Materials Sciences & Engineering Division (MSE); National Science Foundation Graduate Research Fellowship; National Science Foundation (NSF); USDOE
- OSTI Identifier:
- 1611389
- Alternate Identifier(s):
- OSTI ID: 1546357; OSTI ID: 2322519
- Grant/Contract Number:
- SC0010313; DGE-1650441; PHY-1607611; PHY-1125915; de-sc0010313; SC0018946
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Physical Review. B
- Additional Journal Information:
- Journal Volume: 99; Journal Issue: 12; 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; Materials Science; Physics; Chern-Simons gauge theory; Dualities in field theory; Fractional quantum Hall effect
Citation Formats
Hui, Aaron, Kim, Eun-Ah, and Mulligan, Michael. Non-Abelian bosonization and modular transformation approach to superuniversality. United States: N. p., 2019.
Web. doi:10.1103/physrevb.99.125135.
Hui, Aaron, Kim, Eun-Ah, & Mulligan, Michael. Non-Abelian bosonization and modular transformation approach to superuniversality. United States. https://doi.org/10.1103/physrevb.99.125135
Hui, Aaron, Kim, Eun-Ah, and Mulligan, Michael. Wed .
"Non-Abelian bosonization and modular transformation approach to superuniversality". United States. https://doi.org/10.1103/physrevb.99.125135. https://www.osti.gov/servlets/purl/1611389.
@article{osti_1611389,
title = {Non-Abelian bosonization and modular transformation approach to superuniversality},
author = {Hui, Aaron and Kim, Eun-Ah and Mulligan, Michael},
abstractNote = {Quantum Hall inter-plateau transitions are physical exemplars of quantum phase transitions. Near each of these transitions, the measured electrical conductivity scales with the same correlation length and dynamical critical exponents, i.e., the critical points are superuniversal. In apparent contradiction to these experiments, prior theoretical studies of quantum Hall phase transitions within the framework of Abelian Chern-Simons theory coupled to matter found correlation length exponents that depend on the value of the quantum critical Hall conductivity. Here, we use non-Abelian bosonization and modular transformations to theoretically study the phenomenon of superuniversality. Specifically, we introduce a new effective theory that has an emergent U(N) gauge symmetry with any N > 1 for a quantum phase transition between an integer quantum Hall state and an insulator. We then use modular transformations to generate from this theory effective descriptions for transitions between a large class of fractional quantum Hall states whose quasiparticle excitations have Abelian statistics. We find the correlation length and dynamical critical exponents are independent of the particular transition within a controlled 't Hooft large N expansion, i.e., superuniversal! Furthermore, we argue that this superuniversality could survive away from this controlled large N limit using recent duality conjectures.},
doi = {10.1103/physrevb.99.125135},
journal = {Physical Review. B},
number = 12,
volume = 99,
place = {United States},
year = {Wed Mar 20 00:00:00 EDT 2019},
month = {Wed Mar 20 00:00:00 EDT 2019}
}
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