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Title: Exact Boson-Fermion Duality on a 3D Euclidean Lattice

Abstract

The idea of statistical transmutation plays a crucial role in descriptions of the fractional quantum Hall effect. However, a recently conjectured duality between a critical boson and a massless two-component Dirac fermion extends this notion to gapless systems. This duality sheds light on highly nontrivial problems such as the half-filled Landau level, the superconductor-insulator transition, and surface states of strongly coupled topological insulators. Although this boson-fermion duality has undergone many consistency checks, it has remained unproven. Here, we describe the duality in a nonperturbative fashion using an exact UV mapping of partition functions on a 3D Euclidean lattice.

Authors:
 [1];  [1];  [1];  [2]
  1. Stanford Univ., CA (United States). Stanford Inst. for Theoretical Physics
  2. Stanford Univ., CA (United States). Stanford Inst. for Theoretical Physics; SLAC National Accelerator Lab., Menlo Park, CA (United States)
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); Gordon and Betty Moore Foundation (GBMF)
OSTI Identifier:
1417630
Alternate Identifier(s):
OSTI ID: 1415883
Grant/Contract Number:  
GBMF4302; AC02-76SF00515
Resource Type:
Journal Article: Accepted Manuscript
Journal Name:
Physical Review Letters
Additional Journal Information:
Journal Volume: 120; Journal Issue: 1; 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

Citation Formats

Chen, Jing-Yuan, Son, Jun Ho, Wang, Chao, and Raghu, S. Exact Boson-Fermion Duality on a 3D Euclidean Lattice. United States: N. p., 2018. Web. doi:10.1103/PhysRevLett.120.016602.
Chen, Jing-Yuan, Son, Jun Ho, Wang, Chao, & Raghu, S. Exact Boson-Fermion Duality on a 3D Euclidean Lattice. United States. doi:10.1103/PhysRevLett.120.016602.
Chen, Jing-Yuan, Son, Jun Ho, Wang, Chao, and Raghu, S. Fri . "Exact Boson-Fermion Duality on a 3D Euclidean Lattice". United States. doi:10.1103/PhysRevLett.120.016602. https://www.osti.gov/servlets/purl/1417630.
@article{osti_1417630,
title = {Exact Boson-Fermion Duality on a 3D Euclidean Lattice},
author = {Chen, Jing-Yuan and Son, Jun Ho and Wang, Chao and Raghu, S.},
abstractNote = {The idea of statistical transmutation plays a crucial role in descriptions of the fractional quantum Hall effect. However, a recently conjectured duality between a critical boson and a massless two-component Dirac fermion extends this notion to gapless systems. This duality sheds light on highly nontrivial problems such as the half-filled Landau level, the superconductor-insulator transition, and surface states of strongly coupled topological insulators. Although this boson-fermion duality has undergone many consistency checks, it has remained unproven. Here, we describe the duality in a nonperturbative fashion using an exact UV mapping of partition functions on a 3D Euclidean lattice.},
doi = {10.1103/PhysRevLett.120.016602},
journal = {Physical Review Letters},
issn = {0031-9007},
number = 1,
volume = 120,
place = {United States},
year = {2018},
month = {1}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record

Citation Metrics:
Cited by: 17 works
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Figures / Tables:

Figure 1: Figure 1:: (a) The various terms that arise on a link in the exact expansion of Grassmann fields in ZW. From top to bottom, the contributions are: hopping ̄χn+ˆμ−σμ−1/2χn, hopping ̄χnσμ−1/2χn+ˆμ, double hopping plus interaction (1 + U)( ̄χn+μ-σμ−1/2χn+ˆμ)( ̄χn+ˆμ−σμ−1/2χn). (b) In a Grassmann integral, each fermion component mustmore » appear exactly once. Consider a conjugate pair of fermion components, say χn↑ and ̄χn↑. They either appear together in a mass term, or appear separately in two link terms. So the link terms always form closed loops. If this condition is not satisfied as in (c), the contribution vanishes by Grassmann algebra. Thus, all contributions to ZW manifestly satisfy Gauss’s law. (The lattice is 3D. We drew a 2D lattice for clarity.)« less

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