Cooperative shielding in many-body systems with long-range interaction

TL;DR

This paper introduces the concept of Cooperative Shielding in long-range interacting many-body systems, explaining how shielded subspaces influence the propagation of perturbations and reconcile seemingly contradictory experimental and theoretical observations.

Contribution

It uncovers the phenomenon of Cooperative Shielding, showing how shielded subspaces emerge with system size and affect dynamics, linking it to quantum Zeno effects.

Findings

Shielded subspaces emerge as system size increases.

Propagation can be suppressed or quasi-instantaneous depending on initial state.

Effective Zeno Hamiltonian describes short-range dynamics within subspaces.

Abstract

In recent experiments with ion traps, long-range interactions were associated with the exceptionally fast propagation of perturbation, while in some theoretical works they have also been related with the suppression of propagation. Here, we show that such apparently contradictory behavior is caused by a general property of long-range interacting systems, which we name "Cooperative Shielding". It refers to shielded subspaces that emerge as the system size increases and inside of which the evolution is unaffected by long-range interactions for a long time. As a result, the dynamics strongly depends on the initial state: if it belongs to a shielded subspace, the spreading of perturbation satisfies the Lieb-Robinson bound and may even be suppressed, while for initial states with components in various subspaces, the propagation may be quasi-instantaneous. We establish an analogy between the shielding effect and the onset of quantum Zeno subspaces. The derived effective Zeno Hamiltonian successfully describes the short-ranged dynamics inside the subspaces up to a time scale that increases with system size. Cooperative Shielding can be tested in current experiments with trapped ions.