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Nearly-linear light cones in long-range interacting quantum systems



Michael S. Foss-Feig, Zhexuan Gong, Charles W. Clark, Alexey V. Gorshkov


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.
Physical Review Letters


Non-equilibrium, Light-cones, Quantum


Foss-Feig, M. , Gong, Z. , Clark, C. and Gorshkov, A. (2015), Nearly-linear light cones in long-range interacting quantum systems, Physical Review Letters, [online], (Accessed July 23, 2024)


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Created April 13, 2015, Updated November 26, 2018