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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.