title: Cooperative Shielding in Many-Body Systems with Long-Range Interaction.
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.
authors.affiliation: Department of Physics, Yeshiva University, New York, New York 10016, USA and ITAMP, Harvard-Smithsonian Center for Astrophysics, Cambridge, Massachusetts 02138, USA.
authors.forename: Lea F
authors.initials: LF
authors.lastname: Santos
authors.affiliation: Dipartimento di Matematica e Fisica and ILAMP, Universitá Cattolica del Sacro Cuore, 25121 Brescia, Italy and Istituto Nazionale di Fisica Nucleare, sez. Pavia, 27100 Pavia, Italy.
authors.forename: Fausto
authors.initials: F
authors.lastname: Borgonovi
authors.affiliation: Dipartimento di Matematica e Fisica and ILAMP, Universitá Cattolica del Sacro Cuore, 25121 Brescia, Italy and Istituto Nazionale di Fisica Nucleare, sez. Pavia, 27100 Pavia, Italy.
authors.forename: Giuseppe Luca
authors.initials: GL
authors.lastname: Celardo