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

TL;DR

This paper introduces a qubit regularization model using a two-dimensional loop-gas system to emulate the asymptotically free quantum field theory at the BKT transition, reducing finite size effects without fine-tuning.

Contribution

It presents a novel loop-gas model that reproduces universal properties of the BKT transition without fine-tuning, demonstrating qubit regularization of asymptotically free theories.

Findings

Reproduces the universal step-scaling function of the XY model

Shows smaller finite size effects at the BKT transition

Provides a qubit regularization approach for asymptotically free theories

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.