Abstract: In non-relativistic quantum mechanics, if a system has short-range
interactions, an effective speed limit emerges in the form of so-called
Lieb-Robinson bounds. In their essence, these bounds mean that information
is confined (within exponential accuracy) to a light-cone-like structure.
But what happens when interactions become long-ranged? In that case, the
Lieb-Robinson theorem does not hold any more. Studying local quantum
quenches in the transverse Ising model with variable power-law interactions,
we find three qualitatively different regimes, with a complete break-down of
the light-cone-like behaviour in one of them. These regimes are independent
of the underlying ground-state phase and can be explained through the
quasi-particle dispersion relation.
I also report on very recent experimental observations of these effects in
highly tuneable experiments with trapped ions.
Petar Jurcevic et al., in preparation
Philipp Hauke, Luca Tagliacozzo, Spread of correlations in long-range
interacting quantum systems, Phys. Rev. Lett. 111, 207202 (2013)