%0 Journal Article %J Physical Review B %D 2016 %T Causality and quantum criticality with long-range interactions %A Mohammad F. Maghrebi %A Zhe-Xuan Gong %A Michael Foss-Feig %A Alexey V. Gorshkov %X Quantum lattice systems with long-range interactions often exhibit drastically different behavior than their short-range counterparts. In particular, because they do not satisfy the conditions for the Lieb-Robinson theorem, they need not have an emergent relativistic structure in the form of a light cone. Adopting a field-theoretic approach, we study the one-dimensional transverse-field Ising model and a fermionic model with long-range interactions, explore their critical and near-critical behavior, and characterize their response to local perturbations. We deduce the dynamic critical exponent, up to the two-loop order within the renormalization group theory, which we then use to characterize the emergent causal behavior. We show that beyond a critical value of the power-law exponent of long-range interactions, the dynamics effectively becomes relativistic. Various other critical exponents describing correlations in the ground state, as well as deviations from a linear causal cone, are deduced for a wide range of the power-law exponent. %B Physical Review B %V 92 %P 125128 %8 2016/03/17 %G eng %U http://arxiv.org/abs/1508.00906 %N 12 %R 10.1103/PhysRevB.93.125128