Treelike Interactions and Fast Scrambling with Cold Atoms

Area of Science:

• Quantum physics
• Many-body systems
• Quantum information science

Background:

• Quantum scrambling describes the spreading of quantum information.
• Understanding emergent geometries in quantum systems is crucial.
• Experimental realization of complex quantum models is advancing.

Purpose of the Study:

• To propose an experimentally realizable quantum spin model exhibiting fast scrambling.
• To investigate the transition between linear and ultrametric geometries.
• To explore the relationship between geometry, entanglement, and quantum information spread.

Main Methods:

• Developing a quantum spin model with nonlocal interactions (power-of-2 separations).
• Controlling coupling strengths to tune system geometry.
• Analyzing quench dynamics and entanglement entropy calculations.

Main Results:

• The model demonstrates fast scrambling.
• A continuous transition from linear to ultrametric (treelike) geometry is achieved.
• A peak in entanglement and exponentially fast quantum information spreading are observed between regimes.
• The transition is detectable via quench dynamics and entanglement entropy.

Conclusions:

• The proposed model provides an experimental platform for studying emergent quantum geometry.
• Fast scrambling and tunable geometry are key features of the model.
• The findings offer insights into quantum information dynamics in complex systems.