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Asymptotic Freedom at the Berezinskii-Kosterlitz-Thouless Transition without Fine-Tuning Using a Qubit

Sandip Maiti1,2, Debasish Banerjee1,2, Shailesh Chandrasekharan3

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Summary
This summary is machine-generated.

We introduce a novel hard-core loop-gas model to regularize quantum field theories near the Berezinskii-Kosterlitz-Thouless transition. This model reproduces universal behavior without fine-tuning and exhibits reduced finite-size effects.

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Area of Science:

  • * Statistical Mechanics
  • * Quantum Field Theory
  • * Condensed Matter Physics

Background:

  • * The Berezinskii-Kosterlitz-Thouless transition is a critical phenomenon in 2D systems.
  • * Continuum quantum field theories emerging at this transition are often asymptotically free and massive.
  • * Regularization methods are crucial for studying these theories.

Purpose of the Study:

  • * To propose a new two-dimensional hard-core loop-gas model.
  • * To regularize asymptotically free massive continuum quantum field theories.
  • * To investigate the model's ability to reproduce universal properties near the Berezinskii-Kosterlitz-Thouless transition.

Main Methods:

  • * Development of a two-dimensional hard-core loop-gas model.
  • * Setting the fugacity of Fock-vacuum sites to zero in the thermodynamic limit.
  • * Analysis of step-scaling functions and finite-size effects.

Main Results:

  • * The model successfully reproduces the universal step-scaling function of the classical lattice XY model in the massive phase without fine-tuning.
  • * Smaller finite-size effects are observed for universal quantities at the Berezinskii-Kosterlitz-Thouless transition compared to the traditional XY model.
  • * The model demonstrates qubit regularization of an asymptotically free massive quantum field theory.

Conclusions:

  • * The proposed hard-core loop-gas model offers a viable regularization scheme for quantum field theories.
  • * It provides insights into how asymptotic freedom can emerge as a relevant perturbation without fine-tuning.
  • * The model serves as an example of qubit regularization in Euclidean spacetime.