Qubit regularization of asymptotic freedom

TL;DR

This paper introduces a quantum lattice Hamiltonian called the 'Heisenberg-comb' that regularizes the (1+1)-dimensional non-linear O(3) sigma model, demonstrating potential for quantum simulation of asymptotic freedom.

Contribution

It proposes a novel quantum regularization scheme for the asymptotically free sigma model using only two qubits per site, with evidence from Monte Carlo simulations and quantum circuit descriptions.

Findings

Model reproduces universal step-scaling function up to large correlation lengths

Quantum circuit for time evolution provided, enabling potential quantum simulation

Near-term quantum computers could demonstrate asymptotic freedom

Abstract

We provide strong evidence that the asymptotically free (1+1)-dimensional non-linear O(3) sigma model can be regularized using a quantum lattice Hamiltonian, referred to as the "Heisenberg-comb", that acts on a Hilbert space with only two qubits per spatial lattice site. The Heisenberg-comb consists of a spin-half anti-ferromagnetic Heisenberg-chain coupled anti-ferromagnetically to a second local spin-half particle at every lattice site. Using a world-line Monte Carlo method we show that the model reproduces the universal step-scaling function of the traditional model up to correlation lengths of 200,000 in lattice units and argue how the continuum limit could emerge. We provide a quantum circuit description of time-evolution of the model and argue that near-term quantum computers may suffice to demonstrate asymptotic freedom.