Monopole scaling dimension using Monte-Carlo simulation

Karthik, Nikhil

doi:10.1103/PhysRevD.98.074513

Title: Monopole scaling dimension using Monte-Carlo simulation

Abstract

In this paper, we present a practical Monte Carlo determination of the scaling dimensions Δ_Q of flux Q Abelian monopoles through finite-size scaling analysis of the free energy to introduce the background field of classical Dirac monopole-antimonopole pair at critical points of three-dimensional lattice theories. We validate the method in free fermion theory, and by verifying the particle-vortex duality between the monopole scaling dimension at the inverse-XY fixed point and the charge scaling dimension at the XY fixed point. Finally, at the O(2) Wilson-Fisher fixed point of the XY model, we determine the critical exponents Δ₁ = 0.13(2), Δ₂ = 0.29(1) and Δ₃ = 0.47(2), which we find to be proportional to the finite-size critical spectrum of monopoles on square torus.

Authors:

Karthik, Nikhil ^[1]

Brookhaven National Lab. (BNL), Upton, NY (United States). Physics Department

Publication Date:: Wed Oct 31 00:00:00 EDT 2018

Research Org.:: Brookhaven National Laboratory (BNL), Upton, NY (United States)

Sponsoring Org.:: USDOE Office of Science (SC), Nuclear Physics (NP)

OSTI Identifier:: 1482368

Alternate Identifier(s):: OSTI ID: 1480161

Report Number(s):: BNL-209454-2018-JAAM
Journal ID: ISSN 2470-0010; PRVDAQ

Grant/Contract Number:: SC0012704

Resource Type:: Accepted Manuscript

Journal Name:: Physical Review D

Additional Journal Information:: Journal Volume: 98; Journal Issue: 7; Journal ID: ISSN 2470-0010

Publisher:: American Physical Society (APS)

Country of Publication:: United States

Language:: English

Subject:: 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS

Citation Formats


                    Karthik, Nikhil. Monopole scaling dimension using Monte-Carlo simulation.  United States: N. p., 2018. 
Web.  doi:10.1103/PhysRevD.98.074513.

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                    Karthik, Nikhil. Monopole scaling dimension using Monte-Carlo simulation.  United States.  https://doi.org/10.1103/PhysRevD.98.074513

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                    Karthik, Nikhil. Wed .  
"Monopole scaling dimension using Monte-Carlo simulation".  United States.  https://doi.org/10.1103/PhysRevD.98.074513.  https://www.osti.gov/servlets/purl/1482368.

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@article{osti_1482368,

  title        = {Monopole scaling dimension using Monte-Carlo simulation},

  author       = {Karthik, Nikhil},

  abstractNote = {In this paper, we present a practical Monte Carlo determination of the scaling dimensions ΔQ of flux Q Abelian monopoles through finite-size scaling analysis of the free energy to introduce the background field of classical Dirac monopole-antimonopole pair at critical points of three-dimensional lattice theories. We validate the method in free fermion theory, and by verifying the particle-vortex duality between the monopole scaling dimension at the inverse-XY fixed point and the charge scaling dimension at the XY fixed point. Finally, at the O(2) Wilson-Fisher fixed point of the XY model, we determine the critical exponents Δ1 = 0.13(2), Δ2 = 0.29(1) and Δ3 = 0.47(2), which we find to be proportional to the finite-size critical spectrum of monopoles on square torus.},

  doi          = {10.1103/PhysRevD.98.074513},

  journal      = {Physical Review D},

  number       = 7,

  volume       = 98,

  place        = {United States},

  year         = {Wed Oct 31 00:00:00 EDT 2018},

  month        = {Wed Oct 31 00:00:00 EDT 2018}

}

Copy to clipboard

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Works referenced in this record:

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Works referencing / citing this record:

Curious behavior of three-dimensional lattice Dirac operators coupled to a monopole background
journal, November 2019

Karthik, Nikhil; Narayanan, Rajamani
Physical Review D, Vol. 100, Issue 9
DOI: 10.1103/physrevd.100.094501

A curious behavior of three-dimensional lattice Dirac operators coupled to monopole background
text, January 2019

Karthik, Nikhil; Narayanan, Rajamani
arXiv
DOI: 10.48550/arxiv.1908.05284

Numerical determination of monopole scaling dimension in parity-invariant three-dimensional non-compact QED
text, January 2019

Karthik, Nikhil; Narayanan, Rajamani
arXiv
DOI: 10.48550/arxiv.1908.05500

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Title: Monopole scaling dimension using Monte-Carlo simulation

Abstract

Citation Formats

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

Hybrid Monte Carlo journal, September 1987

Compact gauge fields and the infrared catastrophe journal, October 1975

Spectrum of the Wilson-Fisher conformal field theory on the torus journal, July 2017

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Scaling dimensions of higher-charge monopoles at deconfined critical points journal, November 2015

Vortex tension as an order parameter in three-dimensional U(1) + Higgs theory journal, April 1999

An introduction to lattice gauge theory and spin systems journal, October 1979

Conformal Dimensions via Large Charge Expansion journal, February 2018

Eliminating leading corrections to scaling in the three-dimensional O ( N )-symmetric ϕ 4 model: N = 3 and 4 journal, October 2001

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

Néel-State to Valence-Bond-Solid Transition on the Honeycomb Lattice: Evidence for Deconfined Criticality journal, August 2013

High-precision Monte Carlo study of the 3D XY -universality class journal, August 1999

Magnetic Monopoles book, January 2005

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

Erratum to: Scaling dimensions of monopole operators in the ℂ ℙ N b − 1 $$ \mathrm{\mathbb{C}}{\mathrm{\mathbb{P}}}^{N_b-1} $$ theory in 2 + 1 dimensions journal, March 2016

No evidence for bilinear condensate in parity-invariant three-dimensional QED with massless fermions journal, February 2016

Anomalous dimensions of monopole operators in three-dimensional quantum electrodynamics journal, March 2014

Action of hedgehog instantons in the disordered phase of the (2 + 1)-dimensional CPN−1 model journal, November 1990

Topological Disorder Operators in Three-Dimensional Conformal Field Theory journal, November 2002

Critical behavior of the three-dimensional XY universality class journal, May 2001

On the CFT operator spectrum at large global charge journal, December 2015

Scaling dimensions of monopole operators in the ℂ ℙ N b − 1 $$ \mathbb{C}{\mathrm{\mathbb{P}}}^{N_b-1} $$ theory in 2 + 1 dimensions journal, June 2015

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

Theoretical estimates of the critical exponents of the superfluid transition in He 4 by lattice methods journal, October 2006

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

Universal Signatures of Quantum Critical Points from Finite-Size Torus Spectra: A Window into the Operator Content of Higher-Dimensional Conformal Field Theories journal, November 2016

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

The conformal bootstrap journal, June 2016

Numerical study of duality and universality in a frozen superconductor journal, January 2003

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Explicit Derivation of Duality between a Free Dirac Cone and Quantum Electrodynamics in ( $2 + 1$ ) Dimensions
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Hybrid Monte Carlo
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Compact gauge fields and the infrared catastrophe
journal, October 1975

Spectrum of the Wilson-Fisher conformal field theory on the torus
journal, July 2017

Spectrum of conformal gauge theories on a torus
journal, May 2017

Scaling dimensions of higher-charge monopoles at deconfined critical points
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Vortex tension as an order parameter in three-dimensional U(1) + Higgs theory
journal, April 1999

An introduction to lattice gauge theory and spin systems
journal, October 1979

Conformal Dimensions via Large Charge Expansion
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Eliminating leading corrections to scaling in the three-dimensional O ( N )-symmetric ϕ ⁴ model: N = 3 and 4
journal, October 2001

Particle-vortex duality of two-dimensional Dirac fermion from electric-magnetic duality of three-dimensional topological insulators
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Néel-State to Valence-Bond-Solid Transition on the Honeycomb Lattice: Evidence for Deconfined Criticality
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High-precision Monte Carlo study of the 3D XY -universality class
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A duality web in $2 + 1$ dimensions and condensed matter physics
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