SU(3) Quantum Spin Ladders as a Regularization of the CP(2) Model at Non-Zero Density: From Classical to Quantum Simulation

TL;DR

This paper explores using $SU(3)$ quantum spin ladders as a regularization method for simulating the $ ext{CP}(2)$ model at finite density, providing insights into phase structures relevant for quantum simulations of QCD-like theories.

Contribution

It introduces an $SU(3)$ quantum spin ladder approach as a novel regularization for $ ext{CP}(2)$ models and validates it through classical Monte Carlo simulations at non-zero chemical potential.

Findings

Revealed a rich phase structure with Bose-Einstein condensates.

Identified phases with and without ferromagnetic order.

Demonstrated the potential for quantum simulation of $ ext{CP}(2)$ models.

Abstract

Quantum simulations would be highly desirable in order to investigate the finite density physics of QCD. $(1+1)$-d $\mathbb{C}P(N-1)$ quantum field theories are toy models that share many important features of QCD: they are asymptotically free, have a non-perturbatively generated massgap, as well as $\theta$-vacua. $SU(N)$ quantum spin ladders provide an unconventional regularization of $\mathbb{C}P(N-1)$ models that is well-suited for quantum simulation with ultracold alkaline-earth atoms in an optical lattice. In order to validate future quantum simulation experiments of $\mathbb{C}P(2)$ models at finite density, here we use quantum Monte Carlo simulations on classical computers to investigate $SU(3)$ quantum spin ladders at non-zero chemical potential. This reveals a rich phase structure, with single- or double-species Bose-Einstein "condensates", with or without ferromagnetic order.