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Title: 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:
 [1];  [2];  [3];  [2];  [1]
  1. SLAC National Accelerator Lab., Menlo Park, CA (United States)
  2. Stanford Univ., CA (United States)
  3. 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) (SC-22)
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. doi: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. doi: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 = {2015},
month = {6}
}

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Cited by: 17 works
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