TY - JOUR T1 - Causality and quantum criticality with long-range interactions JF - Physical Review B Y1 - 2016 A1 - Mohammad F. Maghrebi A1 - Zhe-Xuan Gong A1 - Michael Foss-Feig A1 - Alexey V. Gorshkov AB - 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. VL - 92 U4 - 125128 UR - http://arxiv.org/abs/1508.00906 CP - 12 U5 - 10.1103/PhysRevB.93.125128 ER -