Nearly linear light cones in long-range interacting quantum systems.
In nonrelativistic 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∼r/v, thereby defining a linear light cone and giving rise to an emergent notion of locality. In systems with power-law (1/r^{α}) interactions, when α exceeds the dimension D, an analogous bound confines influences to within a distance r only until a time t∼(α/v)logr, 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 bounded by a polynomial for α>2D and become linear as α→∞. 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.
Joint Quantum Institute, NIST/University of Maryland, College Park, Maryland 20742, USA.|Joint Center for Quantum Information and Computer Science, NIST/University of Maryland, College Park, Maryland 20742, USA.
Michael
M
Foss-Feig
Joint Quantum Institute, NIST/University of Maryland, College Park, Maryland 20742, USA.|Joint Center for Quantum Information and Computer Science, NIST/University of Maryland, College Park, Maryland 20742, USA.
Zhe-Xuan
ZX
Gong
Joint Quantum Institute, NIST/University of Maryland, College Park, Maryland 20742, USA.
Charles W
CW
Clark
Joint Quantum Institute, NIST/University of Maryland, College Park, Maryland 20742, USA.|Joint Center for Quantum Information and Computer Science, NIST/University of Maryland, College Park, Maryland 20742, USA.
Alexey V
AV
Gorshkov