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

• URL: http://arxiv.org/abs/2307.06117v2
• Date: Sun, 16 Feb 2025 18:47:20 GMT
• Title: Asymptotic Freedom at the Berezinskii-Kosterlitz-Thouless Transition without Fine-Tuning Using a Qubit Regularization
• Authors: Sandip Maiti, Debasish Banerjee, Shailesh Chandrasekharan, Marina K. Marinkovic,
• Abstract summary: We propose a two-dimensional hard-core loop-gas model as a way to regularize theally free massive quantum field theory. Without fine-tuning, our model can reproduce the universal step-scaling function of the classical lattice XY model in the massive phase. Some of universal quantities at the Berezinskii-Kosterlitz-Thouless transition show smaller finite size effects in our model as compared to the traditional XY model.
• Score: 1.800092018453119
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• Abstract: We propose a two-dimensional hard-core loop-gas model as a way to regularize the asymptotically free massive continuum quantum field theory that emerges at the Berezinskii-Kosterlitz-Thouless transition. Without fine-tuning, our model can reproduce the universal step-scaling function of the classical lattice XY model in the massive phase as we approach the phase transition. This is achieved by lowering the fugacity of Fock-vacuum sites in the loop-gas configuration space to zero in the thermodynamic limit. Some of the universal quantities at the Berezinskii-Kosterlitz-Thouless transition show smaller finite size effects in our model as compared to the traditional XY model. Our model is a prime example of qubit regularization of an asymptotically free massive quantum field theory in Euclidean space-time and helps understand how asymptotic freedom can arise as a relevant perturbation at a decoupled fixed point without fine-tuning.

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