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CP(N-1) Quantum Field Theories with Alkaline-Earth Atoms in Optical Lattices

We propose a cold atom implementation to attain the continuum limit of (1+1)-d CP(N-1) quantum field theories. These theories share important features with (3+1)-d QCD, such as asymptotic freedom and $θ$ vacua. Moreover, their continuum limit can be accessed via the mechanism of dimensional reduction. In our scheme, the CP(N-1) degrees of freedom emerge at low energies from a ladder system of SU(N) quantum spins, where the N spin states are embodied by the nuclear Zeeman states of alkaline-earth atoms, trapped in an optical lattice. Based on Monte Carlo results, we establish that the continuum limit can be demonstrated by an atomic quantum simulation by employing the feature of asymptotic freedom. We discuss a protocol for the adiabatic state preparation of the ground state of the system, the real-time evolution of a false $θ$-vacuum state after a quench, and we propose experiments to unravel the phase diagram at non-zero density.