Long-lived nonthermal states in pumped one-dimensional systems of hard-core bosons

We study a unitary time evolution of a symmetry-broken state in a form of a charge density wave in a finite system of interacting hard-core bosons, which can be mapped onto the XXZ Heisenberg chain. Moreover, we introduce a spatially homogeneous and time-dependent vector potential that mimics a short laser pulse. We establish the range of amplitudes of the vector potential for which the onset of charge density wave order can be controlled. We propose a protocol that reveals nonthermal long-lived states, which are characterized by a nonzero charge density wave order translated by one lattice site with respect to its initial formation. The lifetimes of these states are large in comparison to all typical times given by the parameters of the system. They increase with the number of lattice sites, but are significantly suppressed by the integrability-breaking perturbations. In view of these findings, we speculate that the long-lived nonthermal states exist in the thermodynamic limit.