# A qubit regularization of the $O(3)$ sigma model

## TL;DR

This paper introduces a qubit-based Hamiltonian model for the $O(3)$ sigma model in 2D and 3D, demonstrating that it reproduces known critical behaviors and universality classes of classical lattice models.

## Contribution

The authors develop a qubit regularization of the $O(3)$ sigma model that captures its critical phenomena and universality classes in different spatial dimensions.

## Key findings

- In 2D, the model exhibits a quantum critical point with scale-invariant physics similar to the Wilson-Fisher fixed point.
- In 3D, the model shows mean-field critical exponents at the quantum critical point.
- Modifications allow studying $O(2)$ and $Z_2$ symmetries near their critical points.

## Abstract

We construct a qubit regularization of the $O(3)$ non-linear sigma model in two and three spatial dimensions using a quantum Hamiltonian with two qubits per lattice site. Using a worldline formulation and worm algorithms, we show that in two spatial dimensions our model has a quantum critical point where the well-known scale-invariant physics of the three-dimensional Wilson-Fisher fixed point is reproduced. In three spatial dimensions, we recover mean-field critical exponents at a similar quantum critical point. These results show that our qubit Hamiltonian is in the same universality class as the traditional classical lattice model close to the critical points. Simple modifications to our model also allow us to study the physics of traditional lattice models with $O(2)$ and $Z_2$ symmetries close to the corresponding critical points.