Abstract We investigate quantum entanglement in a non-relativistic critical system by calculating the logarithmic negativity of a class of mixed synovex one grass 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 jolly rancher filled gummies 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.