SU(3) quantum spin ladders as a regularization of the CP(2) model at non-zero density: From classical to quantum simulation

Quantum simulations would be highly desirable in order to investigate the finite density physics of QCD. (1+1)-d CP(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 θ-vacua. SU(N) quantum spin ladders provide an unconventional regularization of CP(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 CP(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.