Space-time symmetric qubit regularization of the asymptotically free two-dimensional O(4) model

TL;DR

This paper investigates space-time symmetric lattice models with finite local Hilbert spaces to reproduce asymptotic freedom in the 2D O(4) model, proposing a qubit regularization as an effective field theory.

Contribution

It introduces a simple qubit-based lattice model that acts as an effective field theory for the 2D O(4) model, capturing asymptotic freedom without requiring the continuum limit.

Findings

Simple models reproduce asymptotic freedom within D-theory formalism.

Qubit regularization can serve as an effective field theory near the continuum limit.

A four-dimensional local Hilbert space model acts as an excellent EFT for the original theory.

Abstract

We explore if space-time symmetric lattice field theory models with a finite Hilbert space per lattice site can reproduce asymptotic freedom in the two-dimensional $O(4)$ model. We focus on a simple class of such models with a five dimensional local Hilbert space. We demonstrate how even the simplest model reproduces asymptotic freedom within the D-theory formalism but at the cost of increasing the size of the Hilbert space through coupling several layers of a two-dimensional lattice. We then argue that qubit regularization can be viewed as an effective field theory (EFT) even if the continuum limit cannot be reached, as long as we can tune the model close enough to the continuum limit where perturbation theory, or other analytical techniques, become viable. We construct a simple lattice model on a single layer with a four dimensional local Hilbert space that acts like an excellent EFT of the original theory.