Lindblad Sachdev-Ye-Kitaev Model Dynamics Reveal Exceptional Points and Non-Monotonic Decay at Small Couplings

The complex behaviour of systems driven far from equilibrium remains a central challenge in modern physics, and recent research sheds new light on the dynamics of strongly interacting quantum systems. Jie-ping Zheng from Shanghai Jiao Tong University, alongside Jorge Dukelsky and Rafael A. Molina from the Instituto de Estructura de la Materia, IEM-CSIC, and Antonio M. García-García from Shanghai Jiao Tong University, investigate the unusual relaxation behaviour of a specific model, the Lindblad Sachdev-Ye-Kitaev model, which describes interacting quantum particles coupled to an external environment. Their work reveals that these unexpected dynamics stem from the presence of ‘exceptional points’ within the system’s underlying energy landscape, points where standard theoretical descriptions break down. This discovery explains why the system’s return to equilibrium can slow down or even reverse as its coupling to the environment increases, and suggests a broader principle governing the approach to equilibrium in many complex quantum systems.

Dissipative Dynamics and Relaxation Rate Calculations

Scientists explored how information is lost from a complex quantum system, the Sachdev-Ye-Kitaev model, as it interacts with its surroundings. They developed a method to calculate the rate at which the system returns to equilibrium after a disturbance, and how quickly it loses memory of its initial state. The research focused on understanding how these rates change as the strength of the environmental interaction is varied. The team investigated the system’s behaviour near a critical value, revealing insights into its fundamental properties. The Sachdev-Ye-Kitaev model serves as a valuable tool for studying complex phenomena, including those related to black holes and exotic materials.

The study considered how interactions with the environment cause the system to lose quantum coherence, a key aspect of its behaviour. Scientists employed a sophisticated mathematical framework, extending calculations to systems with a large number of fundamental particles and ensuring the accuracy of their results through careful averaging and extrapolation. The calculations involved mapping the system’s behaviour onto a mathematical landscape, then identifying the most likely path it would take as it evolved. The team carefully analyzed the numerical results, fitting them to mathematical functions to extract the relaxation rate and understand how it changed with the parameter μ.

They observed that the behaviour of the system changed significantly around a critical value, suggesting a transition in its properties. The results indicate that the system exhibits a critical value at which its behaviour undergoes a qualitative change. Below this value, the system’s behaviour is characterized by oscillations, while above it, the behaviour is simpler. This critical value may be related to a fundamental transition in the system’s properties, potentially linked to its ability to scramble information. They investigated the rate at which the system settles into equilibrium, revealing a complex relationship between this rate and the strength of the environmental interaction. The research demonstrated a first-order dynamical phase transition, which transitioned into a more gradual crossover at larger interaction strengths. The team discovered that these features originate from the presence of exceptional points within the system’s mathematical description.

Exceptional points are locations where the system’s properties undergo qualitative shifts, influencing the decay of quantum states. An analytical calculation, supported by numerical results, revealed that the exceptional point corresponding to the longest-living modes occurs at a specific coupling strength, coinciding with a local maximum of the decay rate. This value marks the onset of a region of anomalous equilibration, where the relaxation rate diminishes as the coupling to the environment increases. Further analysis demonstrated that the transition from a phase transition to a crossover occurs at a larger coupling, corresponding to a proliferation of exceptional points in the low-energy limit of the system’s spectrum.

The team mapped the system’s behaviour onto a mathematical landscape, allowing for detailed analysis of its energy levels. These findings demonstrate a fundamental connection between exceptional points and the dynamics of equilibration in strongly interacting quantum systems. The research establishes a framework for understanding how intrinsic thermalization mechanisms interact with, and eventually give way to, environment-induced equilibration, contributing to a deeper understanding of complex quantum systems and their behaviour in response to external influences.

Exceptional Points Govern Quantum System Decay

This research demonstrates that the dynamics of a complex quantum system, the Sachdev-Ye-Kitaev model, exhibit unusual behaviour when interacting with its environment. Specifically, the rate at which the system settles into equilibrium is not simply proportional to the strength of this interaction, but instead displays a complex relationship. The team discovered that this arises from the presence of exceptional points within the system’s underlying mathematical description, influencing the decay of quantum states. These points, related to the system’s energy levels, appear to govern a transition between regimes where the system’s internal dynamics and the environmental influence dominate.

Further investigation revealed that the emergence of these exceptional points correlates with a change in the system’s behaviour, shifting from a distinct phase transition to a more gradual crossover. This suggests a fundamental link between the system’s internal structure, as defined by these exceptional points, and its response to external influences. The authors acknowledge that the strength of these effects may depend on the specific characteristics of the environment, but anticipate that the underlying principles will hold for strongly interacting systems exhibiting quantum chaos. Future work could explore the universality of these findings in other complex quantum systems and further elucidate the role of exceptional points in non-equilibrium dynamics.