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arXiv:2608.30681

Entanglement-enabled Criticality in One-dimensional Quantum Contact Process

Ya-Xin Xiang, Tianyi Yan, Weibin Li, Yu-Qiang Ma

quant-phSubmitted Aug 31, 2026• Announced Sep 1, 2026• 0 citations
arXivHTMLPDF

Abstract

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.

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cond-mat.stat-mechCross-listedarXiv:2608.10948•Aug 12, 2026
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 contact process is a paradigmatic classical stochastic system displaying critical behavior even in one dimension. It features a nonequilibrium phase transition into an absorbing state that has been widely investigated and shown to belong to the directed percolation universality class. When the same process is considered in a quantum setting, much less is known. So far, mainly semiclassical studies have been conducted and the nature of the transition in low dimensions is still a matter of debate. Also, from a numerical point of view, from which the system may look fairly simple-especially in one dimension-results are lacking. In particular, the presence of the absorbing state poses a substantial challenge, which appears to affect the reliability of algorithms targeting directly the steady state. Here we perform real-time numerical simulations of the open dynamics of the quantum contact process and shed light on the existence and on the nature of an absorbing state phase transition in one dimension. We find evidence for the transition being continuous and provide first estimates for the critical exponents. Beyond the conceptual interest, the simplicity of the quantum contact process makes it an ideal benchmark problem for scrutinizing numerical methods for open quantum nonequilibrium systems.
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.
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 role of quantum fluctuations in modifying the critical behavior of nonequilibrium phase transitions is a fundamental but unsolved question. In this study, we examine the absorbing state phase transition of a 1D chain of qubits undergoing a contact process that involves both coherent and classical dynamics. We adopt a discrete-time quantum model with states that can be described in the stabilizer formalism, and therefore allows for an efficient simulation of large system sizes. The extracted critical exponents indicate that the absorbing state phase transition of this Clifford circuit model belongs to the directed percolation universality class. This suggests that the inclusion of quantum fluctuations does not necessarily alter the critical behavior of nonequilibrium phase transitions of purely classical systems. Finally, we extend our analysis to a non-Clifford circuit model, where a tentative scaling analysis in small systems reveals critical exponents that are also consistent with the directed percolation universality class. Published by the American Physical Society 2024
Probabilistic cellular automata provide a simple framework for exploring classical nonequilibrium processes. Recently, quantum cellular automata have been proposed that rely on the propagation of a one-dimensional quantum state along a fictitious discrete time dimension via the sequential application of quantum gates. The resulting (1+1)-dimensional space-time structure makes these automata special cases of recurrent quantum neural networks which can implement broad classes of classical nonequilibrium processes. Here, we present a general prescription by which these models can be extended into genuinely quantum nonequilibrium models via the systematic inclusion of asynchronism. This is illustrated for the classical contact process, where the resulting model is closely linked to the quantum contact process (QCP), developed in the framework of open quantum systems. Studying the mean-field behavior of the model, we find evidence of an "asynchronism transition," i.e., a sudden qualitative change in the phase transition behavior once a certain degree of asynchronicity is surpassed, a phenomenon we link to observations in the QCP.
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.