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Area of Science:

  • Condensed Matter Physics
  • Quantum Field Theory
  • Statistical Mechanics

Background:

  • The XY model describes systems with O(2) symmetry, relevant in various physical phenomena.
  • Derrick's theorem classically obstructs stable topological particles in scalar field theories in dimensions greater than two.
  • Understanding vortex line behavior is crucial for characterizing phases of matter.

Purpose of the Study:

  • To investigate the spontaneously broken phase of the 3D XY model with a vortex line.
  • To numerically determine the mass of the vortex particle.
  • To explore the validity of Derrick's theorem beyond classical approximations.

Main Methods:

  • Utilized Monte Carlo simulations.
  • Employed field-theoretic calculations.
  • Analyzed magnetization and energy density profiles.

Main Results:

  • Successfully determined the mass of the vortex particle in the O(2)-invariant quantum field theory.
  • Demonstrated that Derrick's theorem's obstruction to stable topological particles does not generally persist beyond the classical level.
  • Provided numerical evidence for stable vortex particle existence.

Conclusions:

  • Stable topological vortex particles can exist in the 3D XY model's spontaneously broken phase.
  • The study challenges the classical limitations imposed by Derrick's theorem in quantum field theories.
  • Numerical results confirm the persistence of topological stability in non-classical regimes.