Quantum Contact Process Demonstrates Bistability and Closing Liouvillian Gap in One-Dimensional Systems

The behaviour of complex systems often hinges on subtle transitions between distinct states, and researchers are now exploring such a shift within a fundamental model of interacting particles. Lin Shang, Shuai Geng, and Xingli Li, alongside Jiasen Jin, all from Dalian University of Technology, investigate a one-dimensional quantum contact process, revealing a clear phase transition between an inactive and an active state. This work demonstrates the existence of a bistable system, where the system can exist in two stable states, and importantly, identifies that accurately determining the system’s final state requires extended observation, as it can initially settle into a long-lived intermediate condition. By carefully accounting for interactions between particles, the team pinpoints the precise conditions under which this transition occurs, offering valuable insight into the dynamics of systems ranging from biological networks to critical phenomena in physics.

The team finds that strong interactions between neighboring components, combined with a narrowing of the system’s energy gap, contribute to this behaviour. Moreover, the research reveals that the system may initially settle into a temporary, long-lived state before reaching its final, stable state, suggesting that simulations require extended observation periods to accurately determine the true steady state. By carefully accounting for correlations within the system, the researchers accurately pinpoint the transition point between these states. This work builds upon existing knowledge of non-equilibrium quantum systems, a field attracting significant attention from both experimentalists and theorists.

Quantum Phase Transition in Open Systems

This research provides a comprehensive investigation into absorbing state phase transitions in open quantum systems, specifically focusing on the quantum contact process in one dimension. This work explores how interactions and the system’s coupling to its environment drive a transition from a fluctuating, active state to a static, absorbing state. The study places this research within a broader context of epidemic modelling, statistical physics of absorbing states, and the unique challenges presented by open quantum systems and dissipative phase transitions.

The team employs a combination of theoretical calculations and numerical simulations to understand the system’s behaviour. They develop a theoretical framework based on existing models for absorbing state transitions and open quantum systems, utilising techniques such as quantum master equations and Lindblad operators to describe dissipation. Crucially, the research involves extensive numerical simulations of the quantum contact process, verifying theoretical predictions and exploring parameter regimes difficult to analyse analytically. These simulations utilise Monte Carlo methods to model the system’s stochastic dynamics, time-dependent simulations to observe its evolution, and a neural network approach to determine critical exponents.

The research presents several key findings, including confirmation of the absorbing state phase transition in the quantum contact process. The team accurately determines the critical exponents using both the coherent anomaly method and the neural network approach, providing information about the universality class of the transition. The determined exponents reveal the system’s behaviour near the critical point and its relationship to other systems. The study also highlights the influence of quantum fluctuations on the transition and compares the results with those obtained for classical contact processes, revealing key differences and similarities. The successful application of neural networks to determine critical exponents represents a significant methodological advance.

The authors employ rigorous methodology and carefully validate their results, presenting a clear and well-written explanation of complex concepts. The findings advance our understanding of absorbing state transitions in open quantum systems, and the use of neural networks for determining critical exponents is a novel and promising approach. Future research directions include extending the study to higher dimensions, investigating the effects of long-range interactions, exploring the behaviour of the system in disordered environments, and investigating different types of dissipation. Furthermore, exploring the possibility of experimentally realising the quantum contact process using quantum platforms and applying the insights gained to other open quantum systems represent exciting avenues for future research. Refinement of the neural network approach and the use of machine learning to map out the full phase diagram of the system also offer promising opportunities.

Bistability and Metastability in One Dimension

This research investigates the behaviour of a one-dimensional system where interactions between components lead to either growth or decay, revealing the existence of stable and unstable states. The team demonstrates that, with strong interactions, the system exhibits bistability, meaning it can exist in either an absorbing state with no activity or an active state with sustained activity. This bistability is linked to the closing of a gap in the system’s energy spectrum, indicating a fundamental change in its behaviour. The findings also highlight the importance of considering the system’s evolution over extended periods, as it may initially settle into a long-lived, temporary state before reaching its true steady state. By systematically accounting for correlations within the system, the researchers accurately determined the point at which the transition between these states occurs. This work provides a detailed understanding of the steady-state phases in this type of system, revealing a phase transition that does not rely on symmetry breaking.

The authors acknowledge that their analysis relies on approximations, specifically the single-site and cluster mean-field methods, which may not capture all complexities of the system. Future research directions include exploring similar processes with both quantum and classical characteristics, and investigating the critical exponents associated with the observed phase transition, potentially through coherent anomaly analysis.