  We investigate quantum entanglement in a non-relativistic critical system by
calculating the logarithmic negativity of a class of mixed states in the
quantum Lifshitz model in one and two spatial dimensions. In 1+1 dimensions we
employ a correlator approach to obtain analytic results for both open and
periodic biharmonic chains. In 2+1 dimensions we use a replica method and
consider spherical and toroidal spatial manifolds. In all cases, the universal
finite part of the logarithmic negativity vanishes for mixed states defined on
two disjoint components. For mixed states defined on adjacent components, we
find a non-trivial logarithmic negativity reminiscent of two-dimensional
conformal field theories. As a byproduct of our calculations, we obtain exact
results for the odd entanglement entropy in 2+1 dimensions.
