Quantum Mean-Field Systems Exhibit Phase Transitions Without Lindbladian Gap Closing in Monitored Dynamics
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The behaviour of complex quantum systems under constant observation represents a fundamental challenge in modern physics, and recent work by Luca Capizzi of Université Paris-Saclay, Riccardo Travaglino of SISSA and INFN, and colleagues sheds new light on this area. The researchers investigate how repeated measurements influence the evolution of many-body quantum systems, particularly those with strong interactions between their constituent parts. They demonstrate the emergence of stable, predictable states within these systems, even as the strength of observation increases, a result that challenges existing understanding. Crucially, this stability arises without the typical requirement of a narrowing energy gap, offering a new pathway to control and understand the dynamics of complex quantum phenomena and potentially paving the way for more robust quantum technologies.
Monitored Quantum Systems Exhibit Novel States Researchers investigate the dynamic behaviour of many-body quantum systems subjected to continuous monitoring, alternating projective measurements with standard quantum evolution. Focusing on models with all-to-all interactions, they developed a comprehensive framework to describe the system’s behaviour as it approaches a large scale, where a classical description naturally emerges. Remarkably, the team uncovered previously unknown stationary states, distinct from the usual equilibrium states expected in isolated quantum systems. These states arise due to the continuous monitoring and feedback inherent in the measurement process, fundamentally altering the system’s long-term behaviour. The framework allows identification of phase transitions between these novel states, even when there is no gap closing, a phenomenon typically associated with conventional quantum phase transitions. This suggests that monitoring can induce qualitatively new behaviour in quantum systems, opening avenues for exploring non-equilibrium quantum phenomena and potentially harnessing measurement for quantum control. The research provides analytical explanation for the emergence of conventional infinite-temperature states in systems of infinite size, a phenomenon surprisingly not linked to the closing of the Lindbladian gap. The interplay between quantum evolution and measurements in many-body quantum systems gives rise to a variety of exotic phenomena, including measurement-induced phase transitions characterised by changes in quantum entanglement, observed in systems like random circuits and long-range interactions. These phenomena are inherently dissipative.
Continuous Monitoring Drives Unusual Quantum Phase Transitions The research focuses on understanding how continuous monitoring affects quantum systems, leading to new phases of matter. The monitoring introduces dissipation and drives the system towards specific states. The researchers use a mean-field approximation, simplifying the many-body problem by focusing on the average behaviour of particles, allowing for analytical and numerical treatment of more complex systems. The investigation explores a realistic scenario where measurements are not perfect, occurring with a probability at each time step. This imperfect measurement modifies the system’s evolution, described by a Lindblad master equation, a standard tool for describing open quantum systems. The process leads to a symmetrization of the quantum state, meaning the system tends towards states with a specific symmetry, which can be non-local, affecting states across space. The researchers also explore the classical limit of the quantum system, representing the quantum state in terms of a phase-space distribution, which describes the probability of finding the system in a particular state. The evolution of this distribution is described by a Fokker-Planck equation, a type of equation describing the diffusion of particles in a random environment. They derive an effective Hamiltonian describing the system’s dynamics in this limit, analysing saddle points and instabilities to determine the stability of different phases. The research demonstrates that continuous monitoring can induce phase transitions in quantum systems even without a gap closing, a departure from traditional condensed matter physics. The monitoring process plays a crucial role in driving the system towards specific states and determining the properties of the different phases. The connection to classical dynamics through the Fokker-Planck equation provides insights into the system’s behaviour and helps to understand the underlying mechanisms driving the phase transitions. The researchers develop a theoretical framework for understanding monitored quantum systems, with potential applications in quantum information processing, quantum simulation, and the development of new quantum technologies.
Unexpected Stationary States in Repeated Measurement This research establishes a novel understanding of many-body systems undergoing repeated measurement and evolution, revealing stationary states that emerge unexpectedly when considering a system of infinite size.
The team developed a framework to explore these dynamics, demonstrating that these new stationary states are distinct from the conventional infinite-temperature state, and arise not through the closing of the Lindbladian gap, but through a different mechanism linked to the system’s spectral properties. Specifically, the analysis reveals a separation between discrete bound states and a continuous spectrum, defined by a threshold energy, and provides analytical results consistent with the Pöschl-Teller potential at a reflectionless point. Further investigation into finite-size systems confirms compatibility between the predictions of the mathematical operator and the properties of the finite-size equation in the low-lying spectrum. The researchers observed a double degeneracy in stationary states at finite sizes, linked to the absence of transitions between states of differing parity, which becomes indistinguishable at infinite sizes. Importantly, the team demonstrated that this behaviour is not associated with the closure of the spectral gap, which remains finite even at large system sizes, challenging conventional expectations. The authors acknowledge that their analysis primarily focuses on the critical point, and extending the investigation to non-zero values of the parameter represents a potential avenue for future research. Additionally, exploring general analytical results for the discrete spectrum in cases beyond the critical point could further refine the understanding of these complex systems. 👉 More information 🗞 Phase Transitions without gap closing in monitored quantum mean-field systems 🧠 ArXiv: https://arxiv.org/abs/2512.04201 Tags: