TY - JOUR
T1 - Nearly-linear light cones in long-range interacting quantum systems
JF - Physical Review Letters
Y1 - 2015
A1 - Michael Foss-Feig
A1 - Zhe-Xuan Gong
A1 - Charles W. Clark
A1 - Alexey V. Gorshkov
AB - In non-relativistic quantum theories with short-range Hamiltonians, a velocity $v$ can be chosen such that the influence of any local perturbation is approximately confined to within a distance $r$ until a time $t \sim r/v$, thereby defining a linear light cone and giving rise to an emergent notion of locality. In systems with power-law ($1/r^{\alpha}$) interactions, when $\alpha$ exceeds the dimension $D$, an analogous bound confines influences to within a distance $r$ only until a time $t\sim(\alpha/v)\log r$, suggesting that the velocity, as calculated from the slope of the light cone, may grow exponentially in time. We rule out this possibility; light cones of power-law interacting systems are algebraic for $\alpha>2D$, becoming linear as $\alpha\rightarrow\infty$. Our results impose strong new constraints on the growth of correlations and the production of entangled states in a variety of rapidly emerging, long-range interacting atomic, molecular, and optical systems.
VL - 114
U4 - 157201
UR - http://arxiv.org/abs/1410.3466v1
CP - 15
J1 - Phys. Rev. Lett.
U5 - 10.1103/PhysRevLett.114.157201
ER -