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

Research Question and Approach

This study investigates the nonequilibrium steady-state phase transitions in a one-dimensional hybrid contact process (HCP). The HCP is a model that interpolates between the classical contact process—where excitations spread via stochastic branching and coagulation—and the quantum contact process (QCP), where these processes are driven by coherent unitary operations. The authors aim to determine how the introduction of quantum coherence influences the nature of the phase transition from an absorbing state (where excitations vanish) to an active state (where excitations persist).

To analyze the system, the authors employ a combination of single-site and cluster mean-field (CMF) approximations, Liouvillian spectral analysis, and the coherent anomaly method (CAM). By constructing the Lindblad master equation for a spin-1/2 chain, they map the steady-state phase diagram and identify the stability of different phases using Jacobian matrix analysis.

The researchers identify three distinct regions in the steady-state phase diagram: an absorbing phase, an active phase, and a bistable region. A key finding is that the transition from the absorbing phase to the bistable region is discontinuous, marked by a saddle-node bifurcation. Conversely, the transition from the absorbing phase to the active phase is continuous.

Unlike standard symmetry-breaking transitions, the continuous transition observed here does not originate from a pitchfork bifurcation of the order parameter. The authors also use the coherent anomaly method to extract critical points and exponents, providing a deeper look at the nonclassical scaling behavior of the system as it approaches the critical threshold.

Understanding the interplay between coherent quantum dynamics and incoherent dissipation is essential for controlling nonequilibrium systems in platforms like Rydberg atoms and superconducting circuits. This paper demonstrates that quantum coherence can fundamentally alter the nature of phase transitions in epidemic-like spreading models, shifting them from continuous to discontinuous regimes. This provides a theoretical framework for predicting how quantum fluctuations can induce bistability and modify critical behavior in open many-body systems.