Quantum Phase Transitions and Noise Effects in Ising Models Revealed.

Research demonstrates that dynamical quantum phase transitions occur in the transverse field Ising model when the magnetic field is rapidly altered between critical points. Noise significantly alters this behaviour, reducing the critical velocity required for these transitions and inducing multi-critical modes, with effects scaling with noise intensity.

The behaviour of complex quantum systems under external influence remains a central question in condensed matter physics, with implications for materials science and quantum computing. Researchers are particularly interested in how quickly a system can change before its behaviour becomes unpredictable, a phenomenon known as dynamical quantum phase transitions (DQPTs). A new investigation, detailed in a paper by Sasan Kheiri, R. Jafari, S. Mahdavifar, Ehsan Nedaaee Oskoee, and Alireza Akbari, explores these transitions within the quantum Ising model, a simplified representation of magnetic materials, but with an added complexity of ‘cluster interactions’ – where groups of spins interact rather than individual ones. Their work, titled ‘Dynamical Phase diagram of the Quantum Ising model with Cluster Interaction Under Noisy and Noiseless Driven field’, demonstrates how the interplay between these interactions, external magnetic fields, and the presence of noise fundamentally alters the conditions under which these DQPTs occur, revealing a nuanced relationship between noise intensity and critical sweep velocities. The team, representing institutions including the Institute for Advanced Studies in Basic Sciences, the University of Kaiserslautern, and the Beijing Institute of Mathematical Sciences and Applications, utilise numerical methods to map the dynamical phase diagram, providing insights into the system’s response to rapid changes in external stimuli.

Understanding non-equilibrium quantum dynamics remains a substantial challenge in modern physics, and researchers continually seek effective methods to manipulate quantum systems. This work investigates the profound influence of classical noise on dynamical quantum phase transitions (DQPTs), challenging conventional approaches and revealing surprising control mechanisms.

The study establishes a foundational understanding of DQPTs within the transverse field Ising model, a standard model in quantum magnetism, incorporating cluster interactions, and meticulously examines how these transitions respond to external noise. Researchers consistently observe DQPTs when the model undergoes rapid parameter changes, provided the initial or final field strength resides between critical points, and define a critical sweep velocity that dictates the onset of these transitions. Crucially, the introduction of noise significantly reduces this critical sweep velocity, enabling faster parameter control and suppressing unwanted phase transitions.

The research challenges the Kibble-Zurek mechanism (KZM), a widely accepted theory describing defect formation during rapid parameter changes, by consistently revealing instances of anti-Kibble-Zurek behaviour. The KZM predicts that rapid changes induce defects, but this work demonstrates noise suppressing defect formation, a counterintuitive result highlighting the complex interplay between noise and quantum dynamics. Researchers demonstrate that by tuning the strength of cluster interactions, they manipulate the points at which the energy gap closes, providing precise control over the system’s behaviour and enabling detailed examination of DQPTs under both noiseless and noisy conditions. Numerical results consistently confirm that DQPTs emerge when the starting or ending point of the parameter change, termed a ‘quench’, lies between critical points, and a critical sweep velocity exists above which these transitions vanish.

The research demonstrates that noise consistently suppresses dynamical phase transitions, enabling faster parameter control and opening new avenues for quantum manipulation. The application of coloured noise, a type of noise with a frequency-dependent power spectrum, allows for tailoring the system’s response and achieving desired outcomes, such as suppressing DQPTs or inducing specific quantum states. Increasing experimental verification confirms the theoretical predictions and demonstrates the feasibility of manipulating quantum systems using classical noise, opening exciting possibilities for developing new quantum technologies and exploring fundamental aspects of quantum mechanics.

The research highlights a significant modification of the model’s dynamical diagram through the introduction of noise, demonstrably lowering the critical sweep velocity and expanding the range of possible system behaviours. This expansion occurs through the emergence of multi-critical modes within the dynamical diagram, regions where the system exhibits complex and potentially useful behaviours. The rate at which the system enters this region of multi-criticality also scales linearly with the square of the noise intensity, reinforcing the significant impact of environmental fluctuations on the system’s behaviour and suggesting a pathway for controlling DQPTs through deliberate noise application. This control allows for precise examination of dynamical quantum phase transitions following both noiseless and noisy ramps of the transverse magnetic field.

The findings reveal a clear relationship between noise intensity and critical sweep velocity, demonstrating a linear decrease with the square of the noise intensity for both weak and strong noise levels. This indicates that increasing noise facilitates the suppression of DQPTs, allowing for faster parameter changes without inducing phase transitions, and provides a quantitative understanding of how noise affects the system’s dynamics. Furthermore, the research identifies the emergence of multi-critical modes within the dynamical diagram due to the influence of noise, expanding the range of possible system behaviours and offering new opportunities for quantum control.