Steady-State Phase Transition in One-Dimensional Quantum Contact Process

We investigate the steady-state phases of the one-dimensional quantum contact process model. We present the Liouvillian gap in the thermodynamic limit and uncover the metastability of the system. Exploiting the mean-field approximations with a novel self-consistent condition based on the effective field, we avoid the interference of the metastable state. We show the feature of saddle-node bifurcation of the order parameter revealing the discontinuous phase transition of the steady state and extract the transition point for an infinite-size system. We show the monotonic decrease of the steady-state magnetic susceptibility by the linked-cluster expansion, which does not support the divergence of the correlation length at the vicinity of the transition point. The present results may be tested in the quantum simulator of Rydberg atoms.