Algebraic approach to fractional quantum Hall effect
Abstract
We construct an algebraic description for the ground state and for the static response of the quantum Hall plateaus with a filling factor ν = N/(2N + 1) in the large N limit. Here, by analyzing the algebra of the fluctuations of the shape of the Fermi surface of the composite fermions, we find the explicit form of the projected static structure (SSF) factor at large N and fixed z = (2N + 1)qℓ B ~ 1, where q is the wave number at which the system is probed, and ℓ B is the magnetic length. When z < 3.8, we obtain the exact universal formula for the projected SSF. The formula does not depend on the particular form of the Hamiltonian.
- Authors:
-
- Oxford Univ. (United Kingdom)
- Univ. of Chicago, IL (United States)
- Publication Date:
- Research Org.:
- Univ. of Chicago, IL (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC), High Energy Physics (HEP) (SC-25)
- OSTI Identifier:
- 1594024
- Alternate Identifier(s):
- OSTI ID: 1488626
- Grant/Contract Number:
- SC0009924; FG02-13ER41958
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Physical Review B
- Additional Journal Information:
- Journal Volume: 98; Journal Issue: 24; Journal ID: ISSN 2469-9950
- Publisher:
- American Physical Society (APS)
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 97 MATHEMATICS AND COMPUTING; Fractional quantum Hall effect; Bosonization; Fermi liquid theory
Citation Formats
Nguyen, Dung Xuan, and Son, Dam Thanh. Algebraic approach to fractional quantum Hall effect. United States: N. p., 2018.
Web. doi:10.1103/PhysRevB.98.241110.
Nguyen, Dung Xuan, & Son, Dam Thanh. Algebraic approach to fractional quantum Hall effect. United States. doi:10.1103/PhysRevB.98.241110.
Nguyen, Dung Xuan, and Son, Dam Thanh. Sat .
"Algebraic approach to fractional quantum Hall effect". United States. doi:10.1103/PhysRevB.98.241110. https://www.osti.gov/servlets/purl/1594024.
@article{osti_1594024,
title = {Algebraic approach to fractional quantum Hall effect},
author = {Nguyen, Dung Xuan and Son, Dam Thanh},
abstractNote = {We construct an algebraic description for the ground state and for the static response of the quantum Hall plateaus with a filling factor ν = N/(2N + 1) in the large N limit. Here, by analyzing the algebra of the fluctuations of the shape of the Fermi surface of the composite fermions, we find the explicit form of the projected static structure (SSF) factor at large N and fixed z = (2N + 1)qℓB ~ 1, where q is the wave number at which the system is probed, and ℓB is the magnetic length. When z < 3.8, we obtain the exact universal formula for the projected SSF. The formula does not depend on the particular form of the Hamiltonian.},
doi = {10.1103/PhysRevB.98.241110},
journal = {Physical Review B},
number = 24,
volume = 98,
place = {United States},
year = {2018},
month = {12}
}
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