Abstract:
In recent years, propagation estimates known as Lieb-Robinson
bounds have been obtained and refined for broad classes of quantum lattice
systems. The bounds express the locality of the dynamics of quantum systems
with short range interactions. Simply stated, the dynamics up to time $t>0$
of an observable involving the degrees of freedom in a bounded region of
space depends in an essential way only on the degrees of freedom located at
distance $d$ less than $vt$. The propagation estimates provide a bound for $v$, which is
called the Lieb-Robinson velocity. This simple property has proved to be a
key element in a number of interesting new results on quantum dynamics
ground states. We will discuss a recent application to the characterization
of gapped ground state phases of quantum spin systems. This is a joint work
with Sven Bachmann, Spyridon Michalakis, and Robert Sims.
