Confinement in a two-dimensional Transverse Field Ising Model

I will discuss the emergence of confinement in the transverse field Ising model on a decorated hexagonal lattice. Using an infinite tensor network state optimised with belief propagation, a quench from a broken symmetry state leads to striking nonthermal behaviour underpinned by persistent oscillations and saturation of the entanglement entropy. I will explain this phenomenon by constructing a minimal model based on the confinement of elementary excitations, which take the form of various flavors of hadronic quasiparticles due to the unique structure of the lattice. This model is in excellent agreement with numerical results. For quenches to larger values of the transverse field and/or from non-symmetry broken states, the system displays the expected signatures of thermalisation: a linear growth of entanglement entropy in time, propagation of correlations and the saturation of observables to their thermal averages. I will discuss how thse results provide a physical explanation for the unexpected simulability of a recent large scale quantum computation on an IBM processor.