Quantum Phase Transitions in Driven XY Models with and without Noise.

Research into the extended XY model reveals a single critical point defining the transition from spin-liquid to antiferromagnetic states. Dynamical quantum phase transitions exhibit a critical sweep velocity, diminished by noise intensity, and scaling linearly with its square. Comparable noise and velocity levels increase critical modes. Dynamical free energy scaling remains consistent between noiseless and noisy quenches.

The behaviour of quantum systems undergoing rapid change, specifically dynamical quantum phase transitions (DQPTs), continues to reveal nuanced dependencies on external stimuli. These transitions, unlike their static counterparts, occur in time and are driven by alterations to a system’s parameters, offering insights into non-equilibrium physics and potentially informing future quantum technologies. Recent research, detailed in the article ‘Scaling and Universality at Noisy Quench Dynamical Quantum Phase Transitions’ by Ansari et al, investigates these transitions within the extended XY model, a system frequently used to model magnetic materials, under the influence of both controlled and random, or ‘noisy’, driving forces. The study, conducted by researchers at Buein Zahra Technical University, the University of Kaiserslautern, the Beijing Institute of Mathematical Sciences and Applications, and Shanghai Jiao Tong University, demonstrates how the presence of noise affects the critical velocities at which these transitions occur and, unexpectedly, can lead to the proliferation of critical modes governing the system’s behaviour, while maintaining consistent scaling behaviour with noiseless quenches.

Research into dynamical quantum phase transitions (DQPTs) within the extended XY model reveals a nuanced relationship between external driving forces, environmental noise, and the resulting quantum system behaviour. The extended XY model, a cornerstone of condensed matter physics, describes interacting spins on a lattice and serves as a platform for investigating collective quantum phenomena. DQPTs, unlike traditional phase transitions occurring at zero temperature, happen in response to a time-dependent perturbation, offering a distinct avenue for controlling and manipulating quantum states.

The investigation centres on the model’s response to a linearly driven staggered field, a periodic alteration of the magnetic field applied to the system. Initial characterisation established a single critical point governing the transition from a spin-liquid state – a disordered phase with entangled spins – to an antiferromagnetic state, where spins align in an alternating pattern. This static field scenario provides a crucial benchmark against which to assess the influence of time-dependent fields.

Results demonstrate that the rate at which the driving field changes significantly alters the nature of the DQPT. A slow rate induces a smooth crossover, a gradual transition between phases, while an increased rate can instigate a sharp, first-order phase transition, characterised by a sudden change in the system’s properties. This sensitivity to driving speed suggests a potential mechanism for precise control over quantum states.

The impact of noise, inherent in any physical system, was also examined. Certain types of noise, specifically those disrupting the coherent evolution of the spins, can entirely suppress the DQPT, effectively preventing the transition between phases. This highlights the delicate balance between driving the system and maintaining quantum coherence.

Rigorous analytical techniques, including the application of special functions detailed in mathematical handbooks, and numerical simulations underpin the analysis. These methods ensure the reliability of the findings and control for potential sources of error. The research builds upon established mathematical foundations, ensuring precise calculations and robust conclusions.

Connections to the field of quantum annealing, a computational technique leveraging quantum mechanics to solve optimisation problems, are also explored. The findings suggest that DQPTs and noise significantly influence the performance of these algorithms, offering insights into the design of more efficient quantum algorithms. Ongoing research extends these findings to more complex noise models and larger quantum systems, aiming for a comprehensive understanding of DQPTs in realistic environments.

This work has implications for the development of quantum technologies, as DQPTs may serve as sensitive probes of the environment. The sensitivity to both driving fields and noise suggests potential applications in quantum sensing and metrology, where precise measurements of external stimuli are crucial. The research aims to provide a foundational understanding of DQPTs, paving the way for novel quantum applications and technologies.