Position-Momentum Duality and Fractional Quantum Hall Effect in Chern Insulators
Abstract
We develop a first quantization description of fractional Chern insulators that is the dual of the conventional fractional quantum Hall (FQH) problem, with the roles of position and momentum interchanged. In this picture, FQH states are described by anisotropic FQH liquids forming in momentum-space Landau levels in a fluctuating magnetic field. The fundamental quantum geometry of the problem emerges from the interplay of single-body and interaction metrics, both of which act as momentum-space duals of the geometrical picture of the anisotropic FQH effect. We then present a novel broad class of ideal Chern insulator lattice models that act as duals of the isotropic FQH effect. The interacting problem is well-captured by Haldane pseudopotentials and affords a detailed microscopic understanding of the interplay of interactions and non-trivial quantum geometry.
- Authors:
-
- SLAC National Accelerator Lab., Menlo Park, CA (United States)
- Stanford Univ., CA (United States)
- Univ. of Wurzburg (Germany)
- Publication Date:
- Research Org.:
- SLAC National Accelerator Lab., Menlo Park, CA (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC), Basic Energy Sciences (BES)
- OSTI Identifier:
- 1185173
- Alternate Identifier(s):
- OSTI ID: 1184426
- Report Number(s):
- SLAC-PUB-16305
Journal ID: ISSN 0031-9007
- Grant/Contract Number:
- AC02-76SF00515
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Physical Review Letters
- Additional Journal Information:
- Journal Volume: 114; Journal Issue: 23; Journal ID: ISSN 0031-9007
- Publisher:
- American Physical Society (APS)
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; MATH, PHYS
Citation Formats
Claassen, Martin, Lee, Ching-Hua, Thomale, Ronny, Qi, Xiao-Liang, and Devereaux, Thomas P. Position-Momentum Duality and Fractional Quantum Hall Effect in Chern Insulators. United States: N. p., 2015.
Web. doi:10.1103/PhysRevLett.114.236802.
Claassen, Martin, Lee, Ching-Hua, Thomale, Ronny, Qi, Xiao-Liang, & Devereaux, Thomas P. Position-Momentum Duality and Fractional Quantum Hall Effect in Chern Insulators. United States. https://doi.org/10.1103/PhysRevLett.114.236802
Claassen, Martin, Lee, Ching-Hua, Thomale, Ronny, Qi, Xiao-Liang, and Devereaux, Thomas P. Thu .
"Position-Momentum Duality and Fractional Quantum Hall Effect in Chern Insulators". United States. https://doi.org/10.1103/PhysRevLett.114.236802. https://www.osti.gov/servlets/purl/1185173.
@article{osti_1185173,
title = {Position-Momentum Duality and Fractional Quantum Hall Effect in Chern Insulators},
author = {Claassen, Martin and Lee, Ching-Hua and Thomale, Ronny and Qi, Xiao-Liang and Devereaux, Thomas P},
abstractNote = {We develop a first quantization description of fractional Chern insulators that is the dual of the conventional fractional quantum Hall (FQH) problem, with the roles of position and momentum interchanged. In this picture, FQH states are described by anisotropic FQH liquids forming in momentum-space Landau levels in a fluctuating magnetic field. The fundamental quantum geometry of the problem emerges from the interplay of single-body and interaction metrics, both of which act as momentum-space duals of the geometrical picture of the anisotropic FQH effect. We then present a novel broad class of ideal Chern insulator lattice models that act as duals of the isotropic FQH effect. The interacting problem is well-captured by Haldane pseudopotentials and affords a detailed microscopic understanding of the interplay of interactions and non-trivial quantum geometry.},
doi = {10.1103/PhysRevLett.114.236802},
journal = {Physical Review Letters},
number = 23,
volume = 114,
place = {United States},
year = {Thu Jun 11 00:00:00 EDT 2015},
month = {Thu Jun 11 00:00:00 EDT 2015}
}
Web of Science
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