%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