Exact Boson-Fermion Duality on a 3D Euclidean Lattice

Chen, Jing-Yuan; Son, Jun Ho; Wang, Chao; Raghu, S.

doi:10.1103/PhysRevLett.120.016602

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:

Chen, Jing-Yuan ^[1]; Son, Jun Ho ^[1]; Wang, Chao ^[1]; Raghu, S. ^[2]

Stanford Univ., CA (United States). Stanford Inst. for Theoretical Physics
Stanford Univ., CA (United States). Stanford Inst. for Theoretical Physics; SLAC National Accelerator Lab., Menlo Park, CA (United States)

Publication Date:: Fri Jan 05 00:00:00 EST 2018

Research Org.:: SLAC National Accelerator Lab., Menlo Park, CA (United States)

Sponsoring Org.:: USDOE Office of Science (SC), Basic Energy Sciences (BES); Gordon and Betty Moore Foundation (GBMF)

OSTI Identifier:: 1417630

Alternate Identifier(s):: OSTI ID: 1415883

Grant/Contract Number:: GBMF4302; AC02-76SF00515

Resource Type:: 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.

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                    Chen, Jing-Yuan, Son, Jun Ho, Wang, Chao, & Raghu, S. Exact Boson-Fermion Duality on a 3D Euclidean Lattice.  United States.  https://doi.org/10.1103/PhysRevLett.120.016602

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                    Chen, Jing-Yuan, Son, Jun Ho, Wang, Chao, and Raghu, S. Fri .  
"Exact Boson-Fermion Duality on a 3D Euclidean Lattice".  United States.  https://doi.org/10.1103/PhysRevLett.120.016602.  https://www.osti.gov/servlets/purl/1417630.

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@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},

  number       = 1,

  volume       = 120,

  place        = {United States},

  year         = {Fri Jan 05 00:00:00 EST 2018},

  month        = {Fri Jan 05 00:00:00 EST 2018}

}

Copy to clipboard

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https://doi.org/10.1103/PhysRevLett.120.016602

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Cited by: 38 works

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Figures / Tables:

Figure 1:: (a) The various terms that arise on a link nμ in the exact expansion of Grassmann fields in Z_W. From top to bottom, the contributions are: hopping ̄χn+ˆμ−σμ−1/2χn, hopping ̄χnσ^μ−1/2χn+ˆμ, double hopping plus interaction (1 + U)( ̄χn+μ-σ^μ−1/2χn+ˆμ)( ̄χn+ˆμ−σμ−1/2χn). (b) In a Grassmann integral, each fermion component mustmore »

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Phases of flavor broken QCD3
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Similar Records

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

Abstract

Citation Formats

Figures / Tables:

The Kosterlitz-Thouless transition in two-dimensional Abelian spin systems and the Coulomb gas journal, December 1981

Explicit Derivation of Duality between a Free Dirac Cone and Quantum Electrodynamics in ( 2 + 1 ) Dimensions journal, June 2016

Is the Composite Fermion a Dirac Particle? journal, September 2015

Bosonization and mirror symmetry journal, October 2016

Self-dual quantum electrodynamics as boundary state of the three-dimensional bosonic topological insulator journal, December 2015

Mott transition in an anyon gas journal, November 1993

Symmetry and Duality in Bosonization of Two-Dimensional Dirac Fermions journal, October 2017

Baryons, monopoles and dualities in Chern-Simons-matter theories journal, February 2016

Continuous transition between fractional quantum Hall and superfluid states journal, June 2014

Large scale physics of the quantum hall fluid journal, October 1991

Absence of neutrinos on a lattice journal, July 1981

More Abelian dualities in 2 + 1 dimensions journal, January 2017

Confinement of quarks journal, October 1974

Comments on global symmetries, anomalies, and duality in (2 + 1)d journal, April 2017

Particle-vortex duality of two-dimensional Dirac fermion from electric-magnetic duality of three-dimensional topological insulators journal, June 2016

Dual Dirac Liquid on the Surface of the Electron Topological Insulator journal, November 2015

A duality web in 2 + 1 dimensions and condensed matter physics journal, November 2016

Effective-Field-Theory Model for the Fractional Quantum Hall Effect journal, January 1989

Incompressible quantum Hall states journal, October 1989

Duality and bosonization of ( 2 + 1 ) -dimensional Majorana fermions journal, May 2017

Level/rank duality and Chern-Simons-matter theories journal, September 2016

Mirror symmetry and the half-filled Landau level journal, December 2015

Chern-Simons currents and chiral fermions on the lattice journal, March 1993

Critical Exponents in 3.99 Dimensions journal, January 1972

Topologically massive gauge theories journal, May 1982

Fractional quantum Hall effect and Chern-Simons gauge theories journal, September 1991

Phase Transition in a Lattice Model of Superconductivity journal, November 1981

Correspondence between two-dimensional bosons and a bulk superconductor in a magnetic field journal, February 1989

Parity anomaly and fermion-boson transmutation in 3-dimensional lattice QED journal, September 1989

Fractional Statistics and the Quantum Hall Effect journal, August 1984

Effective theories of the fractional quantum Hall effect at generic filling fractions journal, November 1990

Particle-Vortex Duality from 3D Bosonization journal, September 2016

Composite-fermion approach for the fractional quantum Hall effect journal, July 1989

Mandelstam-'t Hooft duality in abelian lattice models journal, July 1978

Fermi-Bose Transmutations Induced by Gauge Fields journal, February 1988

Particle-vortex duality in topological insulators and superconductors journal, May 2017

Chern-Simons-matter dualities with SO and USp gauge groups journal, February 2017

Phases of flavor broken QCD3 journal, October 2019

Fermionized parafermions and symmetry-enriched Majorana modes journal, August 2018

Deconfined criticality from the QED 3 -Gross-Neveu model at three loops journal, September 2018

Conformality loss and quantum criticality in topological Higgs electrodynamics in 2 + 1 dimensions journal, October 2019

A web of 2d dualities: ${\bf Z}_2$ gauge fields and Arf invariants journal, January 2019

Three-dimensional dualities with bosons and fermions text, January 2017

A master bosonization duality text, January 2017

Master 3d Bosonization Duality with Boundaries text, January 2018

Phases of Flavor Broken QCD$_3$ text, January 2019

The Kosterlitz-Thouless transition in two-dimensional Abelian spin systems and the Coulomb gas
journal, December 1981

Explicit Derivation of Duality between a Free Dirac Cone and Quantum Electrodynamics in ( $2 + 1$ ) Dimensions
journal, June 2016

Is the Composite Fermion a Dirac Particle?
journal, September 2015

Bosonization and mirror symmetry
journal, October 2016

Self-dual quantum electrodynamics as boundary state of the three-dimensional bosonic topological insulator
journal, December 2015

Mott transition in an anyon gas
journal, November 1993

Symmetry and Duality in Bosonization of Two-Dimensional Dirac Fermions
journal, October 2017

Baryons, monopoles and dualities in Chern-Simons-matter theories
journal, February 2016

Continuous transition between fractional quantum Hall and superfluid states
journal, June 2014

Large scale physics of the quantum hall fluid
journal, October 1991

Absence of neutrinos on a lattice
journal, July 1981

More Abelian dualities in 2 + 1 dimensions
journal, January 2017

Confinement of quarks
journal, October 1974

Comments on global symmetries, anomalies, and duality in (2 + 1)d
journal, April 2017

Particle-vortex duality of two-dimensional Dirac fermion from electric-magnetic duality of three-dimensional topological insulators
journal, June 2016

Dual Dirac Liquid on the Surface of the Electron Topological Insulator
journal, November 2015

A duality web in $2 + 1$ dimensions and condensed matter physics
journal, November 2016

Effective-Field-Theory Model for the Fractional Quantum Hall Effect
journal, January 1989

Incompressible quantum Hall states
journal, October 1989

Duality and bosonization of $(2 + 1)$ -dimensional Majorana fermions
journal, May 2017

Level/rank duality and Chern-Simons-matter theories
journal, September 2016

Mirror symmetry and the half-filled Landau level
journal, December 2015

Chern-Simons currents and chiral fermions on the lattice
journal, March 1993

Critical Exponents in 3.99 Dimensions
journal, January 1972

Topologically massive gauge theories
journal, May 1982

Fractional quantum Hall effect and Chern-Simons gauge theories
journal, September 1991

Phase Transition in a Lattice Model of Superconductivity
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Correspondence between two-dimensional bosons and a bulk superconductor in a magnetic field
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Parity anomaly and fermion-boson transmutation in 3-dimensional lattice QED
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Fractional Statistics and the Quantum Hall Effect
journal, August 1984

Effective theories of the fractional quantum Hall effect at generic filling fractions
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Particle-Vortex Duality from 3D Bosonization
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journal, July 1989

Mandelstam-'t Hooft duality in abelian lattice models
journal, July 1978

Fermi-Bose Transmutations Induced by Gauge Fields
journal, February 1988

Particle-vortex duality in topological insulators and superconductors
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Chern-Simons-matter dualities with SO and USp gauge groups
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Fermionized parafermions and symmetry-enriched Majorana modes
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Deconfined criticality from the ${QED}_{3}$ -Gross-Neveu model at three loops
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Conformality loss and quantum criticality in topological Higgs electrodynamics in $2 + 1$ dimensions
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A web of 2d dualities: ${\bf Z}_2$ gauge fields and Arf invariants
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