Monopole scaling dimension using Monte Carlo

Abstract

We present a viable Monte Carlo determination of the scaling dimensions ${\Delta }_Q$ 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. At the $O(2)$ Wilson-Fisher fixed point, we determine the critical exponents ${\Delta }_1=0.13(2)$, ${\Delta }_2=0.29(1)$ and ${\Delta }_3=0.47(2)$, which we find to be proportional to the finite-size critical spectrum of monopoles on square torus.

References in corpus (6)

• A Duality Web in 2+1 Dimensions and Condensed Matter Physics
• The critical exponents of the superfluid transition in He4
• Conformal dimensions via large charge expansion
• Monopoles in CP(N-1) model via the state-operator correspondence
• Numerical study of duality and universality in a frozen superconductor
• Spectrum of the Wilson-Fisher conformal field theory on the torus

Cited by in corpus (8)

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• QED${}_3$-inspired three-dimensional conformal lattice gauge theory without fine-tuning
• Anomalous dimensions of monopole operators in scalar QED${}_3$ with Chern-Simons term
• Evidence for 3d bosonization from monopole operators
• Monopole hierarchy in transitions out of a Dirac spin liquid
• A curious behavior of three-dimensional lattice Dirac operators coupled to monopole background
• Perturbative computation in a QED${}_3$-inspired conformal abelian gauge model on the lattice