The success of the Standard Model in particle physics demonstrates that nature can effectively be described by a continuous Quantum Field Theory (QFT). However, defining QFTs in a mathematically unambiguous way can be challenging, often requiring short-distance (ultraviolet) regularization, which ultimately needs to be removed. Wilson's argument suggests that continuous QFTs emerge near fixed points in renormalization group flows, leading to the concept of universality, which implies that different regularization methods can yield the same QFT. Apart from the traditional Wilson's regularization of QFTs, there is a growing interest in lattice models with strictly finite local Hilbert spaces, such as the Euclidean qubit regularization, in anticipation of the upcoming era of quantum simulations of QFTs. A non-trivial question is whether we can also recover the physics of fixed points at short length scales, using such regularizations. Specifically, can we recover massive continuum QFTs that are free in the ultraviolet but contain a marginally relevant coupling?

In this talk, I will introduce a fresh perspective on the Berezinskii–Kosterlitz–Thouless (BKT) phase transition in the classical lattice XY model, focusing on its emergence through the mechanisms of renormalization group. I will then move to discuss a dimer model proposed in [1,2], which is a prime example of qubit regularization of an asymptotically free massive quantum field theory in Euclidean space-time. Notably, this model exhibits universal quantities at the BKT transition with smaller finite size effects as compared to the traditional XY model, and helps us understand how asymptotic freedom can arise as a relevant perturbation at a decoupled fixed point without fine-tuning.

[1] Maiti, Banerjee, Chandrasekharan, Marinkovic, Phys.Rev.Lett. 132 (2024) 4, 041601, arXiv:2307.06117

[2] Maiti, Banerjee, Chandrasekharan, Marinkovic, PoS LATT23 arXiv:2401.10157