A qubit regularization of asymptotic freedom without fine-tuning

Title:  A qubit regularization of asymptotic freedom without fine-tuning

Abstract:
Other than commonly used Wilson’s regularization of quantum field theories, the regularizations that explore lattice models with a strictly finite local Hilbert space are becoming popular in the anticipation of the upcoming era of quantum simulations of QFTs. A prominent example is Euclidean qubit regularization, which offers a natural way to recover continuum QFTs that emerge via infrared fixed points of lattice theories. A non-trivial question is whether we can also recover the physics of ultraviolet fixed points, using such regularizations. Specifically, can we recover massive continuum QFTs which are free in the UV but contain a marginally relevant coupling?

In this talk, I will discuss a microscopic model with two layers of dimers with an interlayer dimer fugacity, that captures both the asymptotically free UV physics and the massive low-energy physics of the two-dimensional QFT near the Berezinskii-Kosterlitz-Thouless (BKT) phase transition. We find evidence for a renormalization group flow in our model, where asymptotic freedom arises as a crossover critical phenomenon near the quantum critical point and without fine-tuning. Furthermore, I’ll show that some of the universal quantities at the BKT 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 QFT in Euclidean space-time and will hopefully motivate the search for similar models with exotic RG flows that may describe asymptotic freedom of non-Abelian gauge theories and in particular QCD.