Chaotic Quantum Flows Emerge Without Stability, Research Confirms

Researchers at University of Tokyo, led by Atsushi Oyaizu, demonstrate a significant extension of renormalization group (RG) theory, traditionally employed for analysing the ground-state properties of equilibrium statistical systems, to encompass dynamic quantum processes characterised by dissipation and measurement backaction. This advancement addresses a long-standing challenge in theoretical physics: how to apply RG methods to non-unitary quantum dynamics where the conventional concept of energy conservation breaks down. By implementing coarse-graining in real time, the study reveals a crucial competition between decoherence, the loss of quantum coherence, and coherent quantum behaviour, offering new insights into the behaviour of open quantum systems. The findings identify the emergence of chaotic flows within the RG framework, exemplified by the parity-time (PT) transition, and establish a compelling connection between this transition and the well-known Yang-Lee edge singularity, potentially paving the way for novel explorations of imaginary fields within lattice spin systems using quantum technologies.

Chaotic renormalization group flows and parity-time symmetry breaking reveal a critical threshold

Renormalization group flows describe how physical systems evolve under changes in scale, effectively ‘zooming in’ or ‘zooming out’ to understand the dominant behaviour at different length or energy scales. Traditionally, these flows are expected to converge towards stable fixed points, representing equilibrium states. However, when transitioning from stable convergence to complete disruption, above a critical threshold of h = hc(Γ), chaotic behaviour emerges within the RG flows. This threshold, h = hc(Γ), represents the point at which coherent quantum dynamics, governed by the system’s inherent quantum evolution, overcomes the disruptive influence of measurement-induced decoherence. Consequently, the RG flow loses its stable fixed points, a condition previously assumed to be absent in prior investigations of non-equilibrium systems. The study establishes a direct and previously unrecognised link between this chaotic transition and the spontaneous breaking of parity-time (PT) symmetry within the quantum system. PT symmetry, a branch of non-Hermitian quantum mechanics, describes systems where symmetry is not lost through traditional means but rather through the interplay of measurement and unitary evolution. In the non-chaotic phase, real eigenvalues of the system maintain this PT symmetry, but beyond the critical threshold, this symmetry is broken, indicating a qualitative change in the system’s behaviour. The critical behaviour observed in the vicinity of h = hc(Γ) exhibits a striking correspondence with the Yang-Lee edge singularity, a well-established phenomenon in one-dimensional systems characterised by a divergence in the density of states and a rapid change in physical properties. This connection suggests a potential pathway for realising and studying these phenomena in experimentally accessible lattice spin systems, offering a tangible link between theoretical predictions and potential quantum simulations.

Above the critical threshold, the dominance of coherent quantum dynamics over measurement-induced decoherence leads to the elimination of stable fixed points, fundamentally altering the behaviour of the RG flow. The team’s findings demonstrate a clear correlation between this transition and the spontaneous breaking of PT symmetry, a loss of symmetry arising from the combined effects of measurement and unitary evolution. The preservation of real eigenvalues in the non-chaotic phase ensures PT symmetry, while their complexification beyond h = hc(Γ) signals its breakdown. While the current calculations are primarily focused on single-qubit systems, limiting their immediate translation into practical, scalable quantum technologies, the researchers highlight the potential for extending this work to multi-qubit scenarios. Investigating these more complex systems will be crucial for fully realising the potential of these discoveries and exploring potential applications in areas such as quantum information processing and precision sensing. Understanding the behaviour of multi-qubit systems under similar conditions could reveal emergent phenomena and provide insights into the limitations and possibilities of building robust quantum devices.

Adapting renormalization group methods to analyse quantum systems with measurement-driven energy

The extension of the renormalization group to encompass systems experiencing energy loss through measurement and dissipation represents a significant methodological advancement, providing a deeper and more nuanced understanding of non-equilibrium quantum behaviour. Traditional RG methods are primarily designed for systems at equilibrium, where energy is conserved. Adapting these methods to non-unitary dynamics, where energy is not conserved due to dissipation and measurement, requires careful consideration of the system’s evolution and the appropriate coarse-graining procedure. This adaptation clarifies the intricate interaction between coherent quantum behaviour and decoherence, enabling the exploration of dynamics previously inaccessible to this established technique. Specifically, the emergence of chaotic flows within these systems, linked to the Yang-Lee edge singularity, highlights the potential for critical phenomena in non-equilibrium quantum systems. The Yang-Lee edge singularity, occurring at a specific point in the complex energy plane, represents a critical point where system properties change dramatically, and its connection to the chaotic RG flows suggests a fundamental relationship between non-equilibrium dynamics and critical behaviour.

The authors acknowledge that their current work primarily examines the measurement-induced parity-time transition as a specific example of non-unitary quantum dynamics, leaving open the question of whether these findings universally apply to all such systems or other transitions. Demonstrating broad applicability requires further investigation into diverse systems beyond this specific example, a crucial step towards developing future technologies like more accurate sensors and quantum computers. These investigations will determine if the observed phenomena, the emergence of chaotic RG flows, the connection to PT symmetry breaking, and the link to the Yang-Lee edge singularity, are general characteristics of non-unitary quantum systems or specific to the chosen model. Such a comprehensive understanding will be vital for harnessing the power of quantum mechanics in practical applications and advancing the field of quantum technology, potentially leading to the development of novel quantum devices and algorithms. Further research could also explore the impact of different measurement schemes and dissipation mechanisms on the RG flows, providing a more complete picture of the interplay between coherence and decoherence in open quantum systems.

The research demonstrated an extension of the renormalization group to encompass nonunitary quantum dynamics, which describes systems lacking conserved energy. This adaptation clarifies how coherent quantum behaviour and decoherence interact, allowing scientists to study previously inaccessible dynamics. Results revealed chaotic behaviour in the renormalization group flow when coherent dynamics prevailed, linking this to the Yang-Lee edge singularity. The authors suggest further investigation is needed to determine if these findings apply broadly to all non-unitary quantum systems, using diverse examples beyond the measurement-induced parity-time transition examined in this work.