George Mason Physicists Map Quantum Complexity Phase Diagram of Dicke Model

George Mason University physicists have mapped a phase diagram for the Dicke model, a system describing light-matter interactions, revealing two distinct regimes of dynamic behavior. The research demonstrates a connection between the rate at which information spreads and fundamental shifts within the quantum system; at the transition, the slope of changes coincides with a jump in Krylov entropy. Researchers elucidated this regime change by examining wave packet dynamics in Krylov space, observing a competition between “confinement,” where wave packets bounce, and “deconfinement by Rindler hopping,” described as analogous to gravitational spaghettification. This competition proves sensitive to disorder in Lanczos coefficients, offering a new way to categorize and understand how these systems evolve far from equilibrium.

This is not a gradual change; the study reveals a sharp transition point where the system’s response to external stimuli dramatically alters. The team’s work centers on Krylov complexity, a measure of how quickly information propagates within a quantum system. The model, they note, does not contain random disorder but features both integrable and chaotic limits as the strength of light-matter coupling is tuned. This makes it an ideal system for probing the boundaries between order and chaos in quantum dynamics. Distinctive power-law scaling with the number of spins emerges near the transition. “We obtain the global complexity phase diagram for the Dicke model,” they state, emphasizing the comprehensive nature of their findings. The framework outlined in this research, they believe, can be applied to other quantum many-body systems, potentially offering insights into a wide range of physical phenomena.

Krylov Complexity Measures Operator Growth & Dynamics

Recent investigations into quantum many-body systems have increasingly focused on Krylov complexity as a tool for understanding operator growth, thermalization, and chaotic behavior. Establishing whether, and how, changes in a system’s parameters can trigger a sharp transition in these complexity measures remained an open question until now. Researchers have presented evidence for such a transition by mapping out the complexity phase diagram of the Dicke model, a widely studied system describing the interaction between two-level atoms and a cavity photon mode. The study identified two qualitatively different regimes of dynamics within the Dicke model.

The competition between confinement and deconfinement by Rindler hopping, analogous to gravitational spaghettification, is sensitive to the disorder in Lanczos coefficients. The researchers constructed a phase diagram for the Dicke model. The team’s work builds on recent experimental realizations of the Dicke model in trapped ion arrays and cold-atom cavity QED systems.

Researchers are increasingly focused on understanding how quantum systems evolve after a sudden disturbance, a process known as quench dynamics. Their work, building on experimental realizations using trapped ions and cold atoms, identifies two distinct regimes of dynamic behavior within the model. Previous studies suggested Krylov complexity could signal transitions between different dynamic states, but a definitive link remained elusive. For the first time, we observe non-monotonic and sharp changes in Krylov complexity and entropy as a function of a parameter, which clearly identify the complexity transition. This general procedure reduces the complicated many-body dynamics to a single-particle hopping problem.

Recent work with the Dicke model, a standard for light-matter interaction, reveals a surprising link between information spread and fundamental changes in how a quantum system operates, moving beyond gradual shifts to distinct operational regimes.

The intuitive picture of quantum chaos, a system becoming increasingly unpredictable, doesn’t always align with how complexity actually manifests. Researchers have moved beyond simply observing chaotic behavior to mapping out the complexity phase diagram, identifying two distinct regimes of dynamic behavior. This approach moves beyond simply identifying chaos to characterizing the type of complexity present.