  We study the static entanglement structure in (1+1)-dimensional free
Dirac-fermion theory with Lifshitz symmetry and arbitrary integer dynamical
critical exponent. This model is different from the one introduced in [Hartmann
et al., SciPost Phys. 11, no.2, 031 (2021)] due to a proper treatment of the
square Laplace operator. Dirac fermion Lifshitz theory is local as opposed to
its scalar counterpart which strongly affects its entanglement structure. We
show that there is quantum entanglement across arbitrary subregions in various
pure (including the vacuum) and mixed states of this theory for arbitrary
integer values of the dynamical critical exponent. Our numerical investigations
show that quantum entanglement in this theory is tightly bounded from above.
Such a bound and other physical properties of quantum entanglement are
carefully explained from the correlation structure in these theories. A
generalization to (2+1)-dimensions where the entanglement structure is
seriously different is addressed.
