On the non-integrability of driven-dissipative one-dimensional hard-core bosons

We address the question whether hard-core bosons, equivalent to the XX-model, remain integrable once the system is no longer closed. We consider the lattice version under incoherent local pump and loss and show, using random matrix theory, that the statistics of the complex spacial ratios indicate that the system is chaotic. Further, we show that the model belongs in the AI$^{\dagger}$ universality class of random matrices. In addition to this analysis, we investigate an emergent stripe pattern in the Lindbladian spectrum and relate it to the dissipative parameters of the model.