The $\mathbb{C}$P(2) Model at Non-Zero Chemical Potential

TL;DR

This paper demonstrates that quantum simulation experiments can effectively study quantum field theories at non-zero chemical potential by numerically simulating the (1+1)-d $ ext{CP}(2)$ model, which shares key features with QCD.

Contribution

The paper provides the first numerical simulation of the $ ext{CP}(2)$ model at non-zero chemical potential using quantum spin systems, supporting quantum simulation approaches for quantum field theories.

Findings

Numerical results for particle number density as a function of chemical potential.

Evidence supporting the feasibility of quantum simulation for non-zero chemical potential.

The $ ext{CP}(2)$ model exhibits features similar to QCD, such as asymptotic freedom and topological sectors.

Abstract

Recently the simulation of quantum field theories using man-made physical systems has become realistic. In this publication we present numerical results which support the use of quantum simulation experiments to study quantum field theories at non-zero chemical potential. We have numerically simulated the (1+1)-d $\mathbb{C}$P(2) model, which shares several interesting features with QCD, namely asymptotic freedom, a dynamically generated mass gap and topological sectors, via dimensional reduction of a (2+1)-d microscopic theory of SU(3) quantum spins. Numerical results for the particle number density as a function of chemical potential are presented.