Preparation for quantum simulation of the (1+1) -dimensional O(3) nonlinear σ model using cold atoms

The ($1+1$)-dimensional ($1+1\text{D}$) O(3) nonlinear $\ensuremath{\sigma}$-model is a model system for future quantum lattice simulations of other asymptotically free theories, such as non-Abelian gauge theories. We find that utilizing dimensional reduction can make efficient use of two-dimensional layouts presently available on cold-atom quantum simulators. A different definition of the renormalized coupling is introduced, which is applicable to systems with open boundary conditions and can be measured using analog quantum simulators. Monte Carlo and tensor network calculations are performed to determine the quantum resources required to reproduce perturbative short-distance observables. In particular, we show that a rectangular array of 48 Rydberg atoms with existing quantum hardware capabilities should be able to adiabatically prepare low-energy states of the perturbatively matched theory. These states can then be used to simulate nonperturbative observables in the continuum limit that lie beyond the reach of classical computers.