Steady-state phase transition in one-dimensional quantum contact process

Abstract: We investigate the steady-state phases of the one-dimensional quantum contact process model with local dissipation. Exploiting the single-site and cluster mean-field approximations, we show the bistability of the absorbing and active phases in the system with strong interaction between neighboring sites, accompanied by the closing of the Liouvillian gap in the thermodynamic limit. Moreover we find that, near the transition point, the system may evolve first to the long-lived metastable state before reaching the eventual steady state, suggesting us to prolong the time-evolution in the numerical simulation to find the true steady state. We also present the extrapolated transition point by systematically including the correlations in the system.