Confinement in the Transverse Field Ising model on the Heavy Hex lattice

Abstract: We study 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 we show how a quench from a broken symmetry state leads to striking nonthermal behaviour underpinned by persistent oscillations and saturation of the entanglement entropy. We 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. Our model is in excellent agreement with our numerical results. For quenches to larger values of the transverse field and/or from non-symmetry broken states, our numerical results 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. These results provide a physical explanation for the unexpected simulability of a recent large scale quantum computation.