Logarithmic negativity in Lifshitz harmonic models

Abstract Recently, generalizations of the harmonic lattice model have been introduced as a discrete approximation of bosonic field theories with Lifshitz symmetry with a generic dynamical exponent z . In such models in and -dimensions, we study logarithmic negativity in the vacuum state and also finite temperature states. We investigate various features of logarithmic negativity, such as the universal term, its z -dependence and also its temperature dependence, in various configurations. We present both analytical and numerical evidence for the linear z -dependence of logarithmic negativity in almost all parameter ranges both in and -dimensions. We also investigate the validity of the area law behavior of logarithmic negativity in these generalized models and find that this behavior is still correct for small enough dynamical exponents.