Bose-hubbard Model Study Reveals Zero Critical Exponent in Dynamical Quantum Phase Transitions

The behaviour of quantum systems undergoing rapid change remains a central question in modern physics, and recent work by Jia Li and Yajiang Hao, from the University of Science and Technology Beijing, sheds new light on this phenomenon. The researchers investigate the dynamics of the Bose-Hubbard model, a key system for understanding interacting quantum particles, and demonstrate a critical exponent of zero during a dynamical quantum phase transition. This finding, achieved through detailed analysis of the system’s response to sudden disturbances, reveals a surprising universality in the behaviour of strongly interacting quantum systems, independent of specific model details or initial conditions. The ability to precisely control the timing of these transitions, further enabled by modifications to the system’s potential, represents a significant step towards understanding and manipulating quantum dynamics.

Loschmidt Echo Reveals Critical Exponent of Quench Dynamics

This research investigates dynamical quantum phase transitions within the Bose-Hubbard model, a system known for its complex quantum behaviour, using the Loschmidt echo as a means of observation. Scientists demonstrate that after a sudden change in system parameters, the Loschmidt echo decays in a characteristic way, allowing them to determine the critical exponent governing the transition. Focusing on the strongly interacting limit of the one-dimensional Bose-Hubbard model, the team confirms a critical exponent of two, aligning with theoretical predictions and providing insight into the dynamics of strongly correlated quantum systems. This work deepens our understanding of how quantum systems evolve after a sudden change and has implications for quantum information processing and many-body physics.

Through detailed calculations across various system sizes and initial states, the research confirms that the critical behaviour of dynamical quantum phase transitions remains consistent regardless of specific model details or initial conditions. Furthermore, the findings reveal that modifying the harmonic potential well not only preserves the phase transition but also allows for precise control over the timing of the transition.

Driven Systems Exhibit Many-Body Localization

This research explores dynamical quantum phase transitions and their connection to many-body localization, a phenomenon where quantum systems fail to reach thermal equilibrium. The study focuses on driven systems, those subjected to time-periodic forces, adding complexity to their behaviour. The work connects theoretical concepts to experiments using ultracold atoms in optical lattices, making it highly relevant to current research. Scientists leverage Floquet theory, a powerful tool for analysing time-periodic systems, and the Loschmidt echo, a key indicator of dynamical quantum phase transitions.

The research demonstrates the existence of dynamical quantum phase transitions in various driven systems, including those with disorder. A central finding is the link between dynamical quantum phase transitions and many-body localization, suggesting that dynamical quantum phase transitions can serve as a signature of the transition to a many-body localized phase. This provides a potential method for detecting many-body localization in experiments. The importance of disorder in driving both dynamical quantum phase transitions and many-body localization is highlighted.

The study focuses on spin chain models and disordered systems, where the strength of the disorder plays a crucial role. The findings connect directly to experiments with ultracold atoms in optical lattices, offering a clear path for experimental verification. Rydberg atom arrays are suggested as a potential platform for realizing these theoretical models and observing the predicted phenomena.

Bose-Hubbard Model Exhibits Zero Critical Exponent

This research presents a detailed investigation of dynamical quantum phase transitions in the Bose-Hubbard model, employing the Loschmidt echo as a key observable. Scientists demonstrate that following a sudden change in system parameters, the Loschmidt echo exhibits sharp changes, revealing a critical exponent of zero and a logarithmically divergent rate function near the critical point. This finding distinguishes the Bose-Hubbard model from traditional spin models, where a non-zero critical exponent is typically observed, and establishes a unique characteristic of its dynamical behaviour.

Extensive calculations across various system sizes and initial states confirm the universality of this critical exponent, indicating its independence from specific model details or starting conditions. Importantly, the team found remarkable consistency in the short-time dynamical evolution between small and large systems, suggesting that smaller systems can serve as viable models for studying these transitions, significantly easing experimental challenges. Analysis of long-time dynamics reveals Hilbert space fragmentation, with the ergodic dimension growing exponentially with system size and establishing a dynamical equilibrium after the initial phase transition.