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.
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.
We investigate the steady-state phase transition in a one-dimensional hybrid contact process. We implement the single-site and cluster mean-field approximations based on the effective fields and present all the possible steady states of the system. We show the existence of the stable absorbing and active phases, and the bistable region in the long-time limit. The saddle-node bifurcation is observed at the boundary between the absorbing phase and the bistable region, suggesting a discontinuous phase transition. While the absorbing to active phase transition is continuous. To characterize the nonclassical scaling behavior of the continuous phase transition, we extract the true critical points and exponents by means of the coherent anomaly method.
The contact process is a paradigmatic example of nonequilibrium dynamics, with broad applications ranging from chemistry to sociology. Its quantum counterpart, the quantum contact process (QCP), extends the classical model to include coherent processes. Despite sustained interest, the nature of the transition in the one-dimensional (1D) QCP remains debatable. Here, combining Liouvillian spectral analysis, the tensor jump method, exact quantum jump Monte Carlo, and truncated Wigner simulations, we show that 1D QCP undergoes a continuous absorbing-state phase transition, with critical exponents distinct from the classical case. We further find Liouvillian gap closes well below the critical point, highlighting that spectral gap analysis alone cannot distinguish a phase transition from metastability in the QCP. Crucially, the 1D QCP is weakly entangled, yet even this weak entanglement is indispensable for capturing the correct critical behavior, whereas semiclassical methods artificially stabilize the active state and predict a spurious first-order transition. Our work establishes the quantum origin of the phase transition in the 1D QCP and underscores the essential role of entanglement in dissipative quantum many-body systems.
The one-dimensional pair contact process with a particle source is studied by using dynamical cluster mean-field approximations with sites up to n=12. The results obtained for different levels of approximation become convergent especially for n>or=6 and allow us to derive reliable extrapolations to the limit n--> infinity. At the zero source limit, the critical point exhibits a discontinuity whose magnitude vanishes with 1/n. Coherent anomaly analysis of the data supports the conclusion that the vanishing of the order parameter and the density of isolated particles have the same critical behavior. In contrast to an earlier prediction, the present approximation does not support the existence of critical behavior in the inactive phase where the frozen density of isolated particles depends on the initial state.
We investigate a nonequilibrium phase transition in a dissipative and coherent quantum spin system using the quantum Langevin equation and mean-field theory. Recently, the quantum contact process (QCP) was theoretically investigated using the Rydberg antiblockade effect, in particular, when the Rydberg atoms were excited in s states so that their interactions were regarded as being between the nearest neighbors. However, when the atoms are excited to d states, the dipole-dipole interactions become effective, and long-range interactions must be considered. Here we consider a quantum spin model with a long-range QCP, where the branching and coagulation processes are allowed not only for the nearest-neighbor pairs but also for long-distance pairs, coherently and incoherently. Using the semiclassical approach, we show that the mean-field phase diagram of our long-range model is similar to that of the nearest-neighbor QCP, where the continuous (discontinuous) transition is found in the weak (strong) quantum regime. However, at the tricritical point, we find a new universality class, which was neither that of the QCP at the tricritical point nor that of the classical directed percolation model with long-range interactions. Implementation of the long-range QCP using interacting cold gases is discussed.
The dissipative quantum Rabi model exhibits rich non-equilibrium physics, including a dissipative phase transition from the normal phase to the superradiant phase. In this work, we investigate the stability of the superradiant phase in the presence of a weak spin relaxation. We find that even a weak spin relaxation can render the superradiant phase a superradiant metastable phase, in which symmetry-breaking states are stable only for a finite time. This arises because each spin jump induced by relaxation applies as a strong perturbation to the system, potentially driving the system from a symmetry-breaking state to the symmetry-preserving saddle point with finite probability, before it eventually relaxes back to a symmetry-breaking state. Such dynamical processes lead to a finite lifetime of the symmetry-breaking states and restore the symmetry in the steady state. To substantiate these results, we combine mean-field and cumulant expansion analyses with exact numerical simulations. The lifetimes of the symmetry-breaking states are analyzed in finite-size systems and the conclusions are extrapolated to the thermodynamic limit via finite-size scaling. Our findings establish the metastable nature of the symmetry-breaking states in the dissipative quantum Rabi model and reveal the complexity of the dissipative phase transition beyond their equilibrium counterpart. The mechanisms uncovered here can be generalized to a broad class of open quantum systems, highlighting fundamental distinctions between equilibrium phase transitions and steady-state phase transitions.
Abstract Non-Hermitian (NH) quantum system recently have attracted a lots of attentions theoretically and experimentally. However, the results based on the single-particle picture may not apply to understand the property of NH many-body system. How the property of quantum many-body system especially the phase transition will be affected by the non-Hermiticity remains unclear. Here we study NH quantum contact process (QCP) model, whose effective Hamiltonian is derived from Lindbladian master equation. We show that there is a continuous phase transition induced by the non-Hermiticity in QCP. We also determine the critical exponents β of order parameter, γ of susceptibility and study the correlation and entanglement near phase transition point. We observe that the order parameter and susceptibility display infinitely singularity even for finite size system, since non-Hermiticity endow many-body system with different singular behavior from classical phase transition. Moreover our results show that the phase transition have no counterpart in Hermitian case and belongs to completely different universality class.