Cooperative Shielding in Many-Body Systems with Long-Range Interaction

Area of Science:

• Quantum mechanics
• Condensed matter physics
• Atomic, molecular, and optical physics

Background:

• Conflicting experimental and theoretical findings exist regarding the impact of long-range interactions on perturbation propagation in ion trap systems.
• Previous studies have linked long-range interactions to both exceptionally fast and suppressed propagation speeds.

Purpose of the Study:

• To resolve the apparent contradiction in how long-range interactions affect perturbation propagation.
• To introduce and explain the concept of 'cooperative shielding' in systems with long-range interactions.

Main Methods:

• Theoretical analysis of systems with long-range interactions.
• Introduction of the concept of shielded subspaces.
• Establishment of an analogy with quantum Zeno subspaces.
• Derivation of an effective Zeno Hamiltonian.

Main Results:

• Identified 'cooperative shielding' as a general property of long-range interacting systems.
• Demonstrated that shielded subspaces emerge with increasing system size, delaying the effect of long-range interactions.
• Showed that dynamics depend on initial states: shielded states exhibit Lieb-Robinson bound-limited or suppressed spread, while mixed states show quasi-instantaneous propagation.
• The derived effective Zeno Hamiltonian accurately describes short-range dynamics within subspaces.

Conclusions:

• Cooperative shielding reconciles contradictory observations of perturbation propagation in long-range interacting systems.
• The phenomenon offers a new perspective on quantum dynamics and state evolution.
• Cooperative shielding is experimentally verifiable in current trapped-ion experiments.